Selective modulation of intracellular effects of cells using pulsed electric fields

ABSTRACT

A system and method for selectively treating aberrant cells such as cancer cells through administration of a train of electrical pulses is described. The pulse length and delay between successive pulses is optimized to produce effects on intracellular membrane potentials. Therapies based on the system and method produce two treatment zones: an ablation zone surrounding the electrodes within which aberrant cells are non-selectively killed and a selective treatment zone surrounding the ablation zone within which target cells are selectively killed through effects on intracellular membrane potentials. As a result, infiltrating tumor cells within a tumor margin can be effectively treated while sparing healthy tissue. The system and method are useful for treating various cancers in which solid tumors form and have a chance of recurrence from microscopic disease surrounding the tumor.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application relies on the disclosure of and claims priority to and the benefit of the filing date of U.S. Provisional Application No. 61/992,023 filed May 12, 2104, the disclosure of which is hereby incorporated by reference herein in its entirety.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention is related to medical therapies involving the administering of electrical treatment energy. Embodiments of the present invention relate to a system and method that produces two treatment zones: a first zone surrounding the electrodes within which cells are killed non-selectively and a second selective treatment zone surrounding the first zone within which cells are killed selectively, such as aberrant cells. In specific embodiments, systems and methods for selectively treating cells, such as cancer cells, through administration of a train of electrical pulses wherein the pulse length and delay between successive pulses is optimized to produce effects on intracellular membrane potentials are provided. Through the systems and methods of the invention, infiltrating tumor cells disposed within a tumor margin can be effectively treated while sparing healthy tissue within the tumor margin.

Description of Related Art

Focal ablation techniques typically attack tumors by destroying cancerous cells within a well-defined region. Typically, these techniques destroy all of the cells and tissue structure within the treated volume, not just the cancerous cells. A major challenge of focal ablation technologies is that there is typically a region surrounding the tumor which contains healthy cells and some infiltrative cancerous cells. These infiltrative cancer cells, if untreated, may lead to recurrence of the tumor. The solution, in traditional surgical resection and focal ablation, is to treat beyond the tumor margin in an attempt to also remove these infiltrative cancer cells. This presents a major challenge for tumors which typically arise near critical structures, such as blood vessels and nerves. Thus, there is a need in the art for new electroporation protocols that overcome these limitations.

SUMMARY OF THE INVENTION

The present invention provides a system and method of treating infiltrative cancer cells in a tumor margin. This bimodal enhanced ablation mechanism (BEAM) platform uses burst of high frequency electric fields which have been specifically optimized to enhance the intracellular effects of the pulse while minimizing effects on healthy tissue. In embodiments, an optimal burst contains constitutive pulses with durations approximately equivalent to the charging time of the cell membrane plus the discharge time of the nuclear envelope. The optimal off-time between pulses is approximately equivalent to the charging time of the cell membrane.

In embodiments, certain cells (malignant) cells can be preferentially targeted based on their biophysical subcellular structure. Cells with a larger nucleus-to-cytoplasm ratio, which is an indication of their malignancy, are more susceptible to these pulses. The mechanism affecting the cells is related to disrupting their nucleus. Although cell size is the primary parameter for determining when a cell dies under an applied field for typical IRE, in contrast according to embodiments of the present invention, cell size does not play a dominant role.

Specific embodiments provide a method of selectively treating cells, comprising: applying to a tissue a plurality of electrical pulses with a delay between successive pulses, wherein the length of each pulse and the delay between successive pulses are optimized to produce a first treatment zone and a second treatment zone; wherein in the first treatment zone target cells, such as cancer cells, and non-target cells, such as non-cancer cells, are killed and in the second treatment zone the target cells are killed or inhibited while the non-target cells are spared. In such methods, the applying can be performed in vitro, in vivo, or ex vivo.

According to embodiments, within the second treatment zone target cells, such as cancer cells, are inhibited by way of slowed or arrested cell division, or target cells (e.g., cancer cells) are inhibited by way of slowed or arrested migration, or target cells (e.g., cancer cells) are inhibited by way of reduced transport of blood and nutrients, or target cells (e.g., cancer cells) are killed by apoptosis, or some target cells (e.g., cancer cells) are killed or inhibited in the second treatment zone and some non-target cells (e.g., non-cancer cells) are spared in the second treatment zone. In embodiments, the second treatment zone surrounds a tumor and the target cancer cells are infiltrative cells originating from the tumor. The tissue can be brain tissue, and/or the tumor glioblastoma. The target cells in any embodiment of this disclosure can be any type of cells, including for example cancer cells, infiltrative cells, or any undesired cells. The non-target cells can be any type of cell as well and are typically healthy cells, normal cells, or non-cancer cells.

According to embodiments, within the first treatment zone target cells and non-target cells (e.g., cancer cells and non-cancer cells) are killed by necrosis, or some cancer cells and some non-cancer cells are killed in the first treatment zone.

Likewise, according to embodiments both target and non-target cells (e.g., cancer cells and non-cancer cells) can be killed within the first treatment zone as a result of an increase of their transmembrane potential to a lethal threshold.

In embodiments, cancer cells are killed within the second treatment zone as a result of an increase in their nuclear transmembrane potential to a lethal threshold.

In embodiments, the delay between successive pulses can be greater than the length of each pulse, or the delay between successive pulses can be a fraction of the length of each pulse, or the length of each pulse can be equivalent to the charging time of the cell membrane of the cancer cells plus the discharge time of the nuclear membrane of the cancer cells, while the delay between successive pulses is equivalent to the charging time of the cell membrane of the cancer cells. Likewise, the charging time of the cell membrane of the cancer cells and the discharge time of the nuclear membrane of the cancer cells can be determined through numerical modeling.

In embodiments, the pulse train comprises an electric field waveform which is a rectangular pulse, ramp, decaying exponential, or sine wave. In embodiments, the electric field waveform is unipolar or bipolar, or can be a superimposed, bimodal signal comprising a first frequency harmonic and a second frequency harmonic, wherein the second frequency harmonic has a frequency higher than that of the first frequency harmonic.

In embodiments, the electric field waveform comprises alternating nanosecond-order pulses with microsecond order pulses in succession. Likewise, the electric field waveform can be symmetric or asymmetric. The electric field waveform in embodiments can have a carrier frequency in the range of 100 kHz to 10 MHz. The carrier frequency or pulse duration of the waveforms can be based on the cross-over frequency of the cancer cells.

In embodiments, the length of each pulse and the delay between successive pulses are optimized based on the physical nucleus to cytoplasm size ratio of the cancer cells.

Embodiments of the invention include a method of treating cancer in a patient, comprising identifying a solid tumor in a patient, inserting at least one electrode into or adjacent to the solid tumor, and applying a pulse train comprising a plurality of electrical pulses with a delay between successive pulses. Such methods are also applicable to treating undesired cells or target cells that are not necessarily cancerous. In embodiments, the length of each pulse and the delay between successive pulses are optimized to produce a first treatment zone within a radius of the at least one electrode and a second treatment zone between the first radius and a within a second radius of the electrode, which second treatment zone lies outside of the first treatment zone. In the first treatment zone cancer cells and healthy cells are killed non-selectively while in the second treatment zone cancer cells are selectively killed or inhibited an healthy cells are spared. Methods of treating cancer in a patient can be performed in vivo, ex vivo, or in vitro.

In embodiments of the invention, selective inhibition of the cancer cells in the second treatment zone comprises slowed or arrested cell division. Alternatively or in addition, selective inhibition of the cancer cells in the second treatment zone comprises slowed or arrested migration. Alternatively or in addition, selective inhibition of the cancer cells in the second treatment zone comprises reduced transport of blood and nutrients.

In embodiments of the invention, cancer cells and healthy cells are killed within the first treatment zone by necrosis. Alternatively or in addition, cancer cells are killed within the second treatment zone by apoptosis.

In embodiments of the invention, cancer cells and healthy cells are killed within the first treatment zone as a result of an increase of their transmembrane potential to a lethal threshold. Alternatively or in addition, cancer cells are killed within the second treatment zone as a result of an increase in their nuclear transmembrane potential to a lethal threshold.

Preferred embodiments of the invention may target the transmembrane potential of the nucleus, such that it reaches a lethal threshold as a result of the optimized pulses of the invention. However, other embodiments may target any membrane-bound intracellular organelle, whether through effects on the transmembrane potential or any other mechanism, including without limitation the mitochondria, smooth endoplasmic reticulum, rough endoplasmic reticulum, the golgi apparatus, endosomes, lysosomes, peroxisomes, storage vesicles, and transport vesicles.

In embodiments of the invention, the delay between successive pulses is greater than the length of each pulse. Alternatively, the delay between successive pulses is a fraction of the length of each pulse.

In embodiments of the invention, the length of each pulse is equivalent to the charging time of the cell membrane plus the discharge time of the nuclear membrane, while the delay between successive pulses is equivalent to the charging time of the cell membrane. Likewise, embodiments can comprise a multiple of such timing or even a fraction of such timing. The charging time of the cell membrane and the discharge time of the nuclear membrane may be determined through numerical modeling.

In embodiments of the invention, the pulse train comprises an electric field waveform which is a rectangular pulse, ramp, decaying exponential, or sine wave. The electric field waveform may be unipolar or bipolar. The electric field waveform may be a superimposed, bimodal signal comprising a first frequency harmonic (such as a low frequency harmonic) and a second frequency harmonic (such as a high frequency harmonic). The electric field waveform may comprise alternating nanosecond-order pulses with microsecond order pulses in succession. The electric field waveform may be asymmetric. The electric field waveform may have a carrier frequency in the range of 100 kHz to 10 MHz. The carrier frequency or pulse duration of the waveforms may be based on the cross-over frequency of the cancer cells, undesired cells, or otherwise referred to as the target cells.

In embodiments, the length of each pulse and the delay between successive pulses are optimized based on the physical nucleus to cytoplasm size ratio of the cancer cells.

In embodiments of the invention, the pulses are bipolar square waves and the length of each pulse is between 250 nanoseconds and 50 microseconds.

Embodiments of the invention include a method of treating a cancer in a patient, comprising identifying a solid tumor in a patient, inserting at least one electrode into or adjacent to the solid tumor, and applying a pulse train comprising a plurality of electrical pulses, wherein the pulses are bipolar square waves and the length of each pulse is between 250 nanoseconds and 50 microseconds.

Embodiments of the invention include a method of treating a cancer in a patient, comprising identifying a solid tumor in a patient, inserting at least one electrode into or adjacent to the solid tumor, and applying a pulse train comprising a plurality of electrical pulses, wherein the pulse train has an electric field waveform which is a superimposed, bimodal signal comprising a first frequency harmonic and a second frequency harmonic, such as a low frequency harmonic and a high frequency harmonic.

Embodiments of the invention include a system for treating a cancer in a subject, comprising at least one electrode, and a voltage pulse generator operatively coupled to the electrode and configured to apply a pulse train comprising a plurality of electrical pulses, wherein the pulse train has an electric field waveform which is a superimposed, bimodal signal comprising a low frequency harmonic and a high frequency harmonic. The voltage pulse generator may comprise solid state switching devices arranged in a multi-level, neutral point clamped, or cascaded H-bridge topology.

Also included is a method of selectively treating cells, comprising: applying a plurality of electrical pulses as a treatment to a substance containing cells, wherein the pulses are bipolar square waves and the length of each pulse is between 250 nanoseconds and 50 microseconds, with a delay between pulses of between 250 nanoseconds and 50 microseconds; wherein one type of cell is treated and another type of cell is not treated by the plurality of electrical pulses. In embodiments, the treated cells are killed and untreated cells are not killed. The substance containing cells for example can be a tissue, a non-living object, a solution, a body part, or a living or non-living patient, human, animal, or tissue.

In embodiments, provided is a method of selectively treating cells, comprising: applying a pulse train comprising a plurality of electrical pulses to a substance containing cells, wherein the pulse train has an electric field waveform which is a superimposed, bimodal signal comprising a first frequency harmonic and a second frequency harmonic with a frequency higher than that of the first. In embodiments, the pulse train selectively kills cells of a selected type and spares cells of another type.

Systems of the invention include any system configured to implement one or more methods of the invention. Included is a system for selectively treating cells, comprising: at least one electrode; and a voltage pulse generator coupled to the electrode and configured to apply a pulse train comprising a plurality of electrical pulses, wherein the pulse train has an electric field waveform which is a superimposed, bimodal signal comprising a first frequency harmonic and a second frequency harmonic, wherein the second frequency harmonic has a frequency higher than that of the first frequency harmonic.

In embodiments, the voltage pulse generator is configured to select the bimodal signal such that the pulse train selectively kills cells of a selected type and spares cells of another type, or the voltage pulse generator comprises solid state switching devices arranged in a multi-level, neutral point clamped, or cascaded H-bridge topology.

Additional methods include a method of selectively treating cells, the method comprising: delivering electrical pulses to a substance containing cells in a manner sufficient to kill only cells having a selected biophysical subcellular structure. In embodiments, the cells having the selected biophysical subcellular structure have a nucleus and the cells are killed by disrupting the nucleus of the cells. The cells having the selected biophysical subcellular structure can have a selected nucleus-to-cytoplasm area ratio.

A method of selectively treating cells, comprising: applying a plurality of electrical pulses to a substance containing cells, wherein the plurality of electrical pulses has a frequency, amplitude, and pulse waveform selected to treat target cells of one type of cell and spare non-target cells of another type of cell is also included within the scope of the invention. Such methods of the invention can be a selective method wherein cancer cells are treated and normal cells are spared. Such methods can be a palliative method wherein cancer cells of a more malignant type are treated and cancer cells of a less aggressive type are spared.

Methods of the invention can further comprise determining a nucleus-to-cytoplasm ratio for the target cells; and selecting the frequency, amplitude, and pulse waveform based on the nucleus-to-cytoplasm ratio for the target cells. In embodiments the nucleus-to-cytoplasm ratio is measured or otherwise determined from cells taken from a biopsy of the substance containing cells.

A method of selectively ablating malignant cells is included in the invention, the method comprises: determining a first death threshold for malignant cells present in a tissue region; determining a second death threshold for non-malignant cells present in the tissue region; administering electrical pulses to the tissue region at or above the first death threshold and below the second death threshold to kill the malignant cells. In embodiments of methods of the invention, the non-malignant cells are not killed. In embodiments, the malignant cells each comprise a cell nucleus and are killed by administering the electrical pulses in a manner sufficient to disrupt the cell nucleus.

Included in embodiments is a method of enhancing the transport of material into an organelle, comprising: applying a plurality of electrical pulses to a substance containing cells, wherein the plurality of electrical pulses has a frequency, amplitude, and pulse waveform selected to optimize the transport of molecules into an organelle.

According to embodiments, the plurality of electrical pulses includes positive and negative pulses having different pulse widths, or the plurality of electrical pulses includes positive and negative pulses having different amplitude. In embodiments, the organelle is the nucleus, mitochondria, endoplasmic reticulum, vacuole, lysosome, or chloroplast.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate certain aspects of embodiments of the present invention, and should not be used to limit the invention. Together with the written description the drawings serve to explain certain principles of the invention.

FIG. 1 is a schematic diagram showing an ablation zone and a selective therapy zone according to the invention, with the x- and y-axes showing distance in meters.

FIG. 2 is a graph showing the effects of an optimized pulse length and pulse delay on the nuclear transmembrane potential.

FIG. 3 is a graph showing effects of a suboptimal pulse on the nuclear transmembrane potential in a healthy cell and a cancer cell.

FIG. 4 is a schematic diagram and an overlayed graph showing enhanced electrophoretic transfer of a gene with asymmetric pulses.

FIG. 5A is a schematic diagram of cells with two different sized nuclei which serves as a key for FIGS. 5B-5G.

FIG. 5B a graph showing a low frequency bipolar sinusoidal signal.

FIG. 5C is a graph showing a high frequency bipolar sinusoidal signal.

FIG. 5D is a graph showing a bimodal sinusoidal signal comprising the low frequency harmonic of FIG. 5B and a high frequency harmonic of FIG. 5C.

FIG. 5E is a graph showing the nuclear transmembrane potential of cells with two different sized nuclei as a result of the low frequency bipolar sinusoidal signal of FIG. 5B.

FIG. 5F is a graph showing the nuclear transmembrane potential of cells with two different sized nuclei as a result of the high frequency bipolar sinusoidal signal of FIG. 5C.

FIG. 5G is a graph showing the nuclear transmembrane potential of cells with two different sized nuclei as a result of the bimodal sinusoidal signal of FIG. 5D.

FIG. 6 is a schematic diagram of a representative system of the invention.

FIG. 7 is a schematic diagram of a representative control computer for implementing a treatment of the invention.

FIG. 8 is diagram illustrating details of the generator shown in the system of FIG. 6, including elements for detecting an over-current condition and/or an under-current.

FIG. 9 is a graph showing the results of numerical simulation of the transmembrane potential (TMP) of a cell suspended in 1.0 S/m solution under the influence of a 1000V/cm pulsed electric field.

FIG. 10 is a table showing parameter values used in parametric studies on the transmembrane potential (TMP).

FIG. 11 is a graph showing steady state maximum transmembrane potential (TMP) for a MDA-MB-231 cell under a 400 V/cm electic field verses frequency. The red vertical line represents the first crossover frequency of MDA-MB-231 cells in 0.01 S/m conductivity media.

FIGS. 12A and 12B are graphs showing the transmembrane potential (TMP) response to a 1000 V/cm electric field at 100 kHz (FIG. 12A) and 1 MHz (FIG. 12B).

FIG. 13 is a graph showing a transient response to a cell's lipid bilayer to a 1000 V/cm electric field.

FIG. 14 is a graph of a transient response of a cell to a 1000 V/cm electric field.

FIG. 15 is a graph showing the transmembrane potential (TMP) and nuclear transmembrane potential (nTMP) for a cell with a 0.5:1 nucleus to cytoplasm ratio.

FIG. 16 is a graph showing the effect that pulse time has on the nuclear transmembrane potential (nTMP) when the off time between pulses is held to 500 nanoseconds.

FIG. 17 is a graph showing the effect of pulse delay on the nuclear transmembrane potential (nTMP).

FIGS. 18A and 18B are graphs showing pulse geometry can be optimized to increase the nuclear transmembrane potential (nTMP) above the single pulse maximum, where FIG. 18A shows the nTMP as a result of a 500 nanosecond on −500 nanosecond off pulse regimen and FIG. 18B shows the nTMP as a result of a 4 microsecond on −500 nanosecond off pulse regimen.

FIG. 19 is a graph showing the effect of nucleus size on the nuclear transmembrane potential.

FIG. 20 is a graph showing the steady state maximum membrane potential achievable for a sinusoidal signal.

FIG. 21A is a schematic diagram of cells with two different sized nuclei which serves as a key for FIGS. 21B and 21C.

FIG. 21B is a graph showing the nuclear transmembrane potential of cells of two different sized nuclei as result of applying a bimodal sinusoidal signal with an electric field strength of 4000 V/cm.

FIG. 21C is a graph showing the nuclear transmembrane potential of cells of two different sized nuclei as result of applying a bimodal sinusoidal signal with an electric field strength of 5000 V/cm.

FIG. 22 is a graph which illustrates the selective zone of nuclear electroporation. The electric field contours shown are 4000 V/cm (solid line) and 5000 V/cm (dashed line).

FIG. 23A is a graph showing a single sub-microsecond pulse waveform.

FIG. 23B is a graph showing the single sub-microsecond pulse waveform of FIG. 23A repeated 200 times to create an irreversible electroporation pulse train.

FIG. 23C is a graph of the effect of the pulse train of FIG. 23B on cell viability for 1000 V/cm, 2000 V/cm, and 4000 V/cm pulses at 1 hour and 16 hours post-treatment.

FIG. 24 is a graph showing viability of cells treated with 1500 V/cm pulses as a function of pulse length.

FIG. 25 is a graph showing viability of cells treated with 3000 V/cm pulses as a function of pulse length.

FIG. 26 is a graph showing viability of cells treated with 4000 V/cm pulses as a function of pulse length.

FIGS. 27A and 27B are diagrams showing ablation enhancement due to selective targeting, with the x- and y-axes showing distance in meters and with the ablation zone shown in white and the zone of selective targeting enhancement shown in orange (grey, in black and white figures). FIG. 27A shows these zones as a result of 1000 V pulses using in vitro values. FIG. 27B shows these zones as a result of 1000V pulses using equivalent in vivo thresholds.

FIG. 28 is a table showing parameters used in numerical analysis.

FIG. 29A is a schematic of an experimental setup used in Example 2. 100 uL of cell suspension was added to a 2 mm electroporation cuvette. The inset represents mesh used to simulate the cell membrane and nuclear envelope.

FIG. 29B is a schematic of the experimental burst containing a cycling of positive and negative polarity pulses which represents the protocol used for all experiments in Example 2.

FIGS. 30A-30C are graphs showing exemplary waveforms of pulses of different lengths using the experiments in Example 2 which plot applied voltage, U/kV, i as a function of time, t/μs. Each burst has a total on time of 100 μs, with 50 μs energized in each polarity. Representative segments from bursts with 250 ns (FIG. 30A) and 1 μs (FIG. 30B) and 5 μs (FIG. 30C) constitutive pulses.

FIGS. 31A-31C are graphs showing the results of finite element simulations. The applied electric field, E/(kV/cm), voltage drop across the cell membrane, Um/V, and nuclear envelope, Un/V, are presented as a function of time, t/μs. FIG. 31A shows a bi-polar square wave with 50 ns rise and fall times was used to simulate the maximum (FIG. 31B) transmembrane potential of the cell membrane (Um) and (FIG. 31C) nuclear envelope (Un).

FIGS. 32A-C are graphs showing the results of a parametric analysis on the cell membrane potential. The voltage drop across the cell membrane, Um/V, and nuclear envelope, Un/V, are presented as a function of time, t/μs. The effect of varying the (FIG. 32A) Pulse Width, (FIG. 32B) Media Conductivity, (FIG. 32C) Pulse-to-Pulse Delay Time are shown. Dashed lines represent the transmembrane potential of the cell membrane (Um) and solid lines represent the transmembrane potential of the nuclear envelope (Un). Note that the axis for Um and Un have different scales.

FIGS. 33A-33E are graphs showing a cell property parametric analysis. The voltage drop across the cell membrane, Um/V, and nuclear envelope, Un/V, are presented as a function of time, t/μs. The effect of varying the (FIG. 33A) Nucleus-Cytoplasm Ratio, (FIG. 33B) Cytoplasm Conductivity, and (FIG. 33C) Cell Membrane Permittivity are shown. The voltage drop across the cell membrane, Um/V, and nuclear envelope, Un/V, of a benign and cancerous cell are shown in FIGS. 33D and 33E. Note that the axis for Um and Un have different scales.

FIGS. 34A-34D are graphs showing simulation of membrane potentials due to 250 ns and 1 μs experimental pulses. The applied electric field, E/(kV/cm), voltage drop across the cell membrane, U_(m)/V, and nuclear envelope, U_(n)/V, are presented as a function of time, t/μs. FIG. 34A shows a 1.5 kV/cm 250 ns impulse and FIG. 34B shows the resulting transmembrane potential of the cell membrane (U_(m)) and nuclear envelope (U_(n)). FIG. 34C shows a 1.5 kV/cm 1 μs impulse and FIG. 34D shows the resulting transmembrane potential of the cell membrane (U_(m)) and nuclear envelope (U_(n)). Dashed lines represent the transmembrane potential of the cell membrane (U_(m)) and solid lines represent the transmembrane potential of the nuclear envelope (U_(n)).

FIG. 35 is a graph showing change in media temperature during exposure to 4000 V/cm. The change in temperature, ΔT/K, is presented as a function of time, t/s. Bursts with 50 us and 250 ns constitutive pulses resulted in similar temperature rises. ΔT=T−T_(ref), where T_(ref)=20° C.

FIGS. 36A-36C are graphs showing cell death occurs due to immediate and delayed mechanisms. The relative viability, r_(viability), is presented as a function of pulse width, Δt_(p)/μs. Relative viability of cells 1 and 24 hours after exposure to (FIG. 36A) 1500 V/cm, (FIG. 36B) 3000 V/cm, (FIG. 36C) 4000 V/cm bursts. r_(viability)=N_(surviving)/N_(total), normalized to controls, where N is the number of cells. In all experiments cells were exposed to 80 bursts each with an energized time of 100 μs. Error bars represent the standard deviation after a minimum of three (n=3) randomized experiments. Stars (*) denote statistical significance between 1 and 24 hour time points (α≦0.1).

FIGS. 37A-L are graphs showing bursts have cumulative effect on the time membrane potentials are above critical thresholds: The time, t/μs, for which the cell membrane or nuclear envelope is greater than a critical threshold is presented as a function of pulse width, Δt_(p)/μs. FIGS. 37A, B, E, F, I, and J represent the time for which the cell membrane has a potential drop (U_(m)) greater than 1 V. FIGS. 37C, D, G, H, K, and L represent the time for which the nuclear envelope has a potential drop (U_(n)) greater than 0.5, 0.75, or 0.9 V.

FIGS. 38A-38B are schematic diagrams showing traditional monopolar IRE pulse (FIG. 38A) and high frequency bipolar burst (FIG. 38B).

FIG. 38C is a photograph showing experimental setup with electrodes inserted into the 3D tissue mimic.

FIGS. 38D-G are images of live [green] and dead [red] regions of a tissue mimic after treatment with 80 bursts containing (FIG. 38D) 2, (FIG. 38E) 24, and (FIG. 38F) 50 bipolar 2 μs pulses with a 2 μs delay between alternating pulses. FIG. 38G shows diffuse treatment of 50 bipolar 2 μs pulses with 20 ms between alternating pulses. Scale bar represents 2 mm.

FIG. 39 is a table showing tissue mimic experimental parameters.

FIG. 40A is a graph showing lethal electric field threshold for PPT cells in tissue mimic for 2200 V2s dose. FIG. 40B is a graph showing relative viability of PPT cells in media suspension after treatment with 1500 V/cm. Data in FIG. 40B is from Sano et al. 2014 and data labeled ‡ in FIGS. 40A and B is from Arena et al. 2012. FIG. 40C is a graph showing the temperature profile at center of tissue mimic as measured experimentally and predicted numerically.

FIGS. 41A-41D are graphs showing the lethal electric field threshold for the following treatments. FIG. 41A: 540 V and 100 us energized time per burst with 8 or 80 bursts per treatment. 2 and 50 μs groups contained bipolar pulses, 100 μs group had monopolar pulses. FIG. 41B: 2 μs group at 250, 540, and 650V with equivalent energy per burst. FIG. 41C: 2 μs group at 540V with 4, 48, or 100 μs energized per burst. FIG. 41D: 2 μs group at 540 V where inter-burst delay was 1 s [burst] or 20 ms [diffuse]. FIGS. 41B-D: Treatment groups received 80 bursts of treatment for 80 seconds [diffuse group]. Data labeled ‡ is from Arena et al. 2012.

FIGS. 42A-42D are graphs showing tumor volume as a function of days post treatment for (FIG. 42A) Sham group, (FIG. 42B) 1 μs group, (FIG. 42C) 2 μs group, and (FIG. 42D) 5 μs group. FIG. 42E is a graph showing the volume of tumors averaged across all mice for each treatment group.

FIG. 43A is a photograph showing pulses being delivered through needles inserted into the tumor.

FIG. 43B is a photograph showing immediate tumor whitening and FIG. 43C is a photograph showing scab formation after 24 hours that was observed after most treatments.

FIGS. 43D and 43F are photographs showing representative end point images from the sham group. FIGS. 43E and 43G are photographs showing representative end point images from the 5 μs group. The photographs show the existence and absence of subcutaneous tumor 30 days post-treatment. Numbers written on the surface of the skin are for tissue orientation during histological preparation.

FIG. 43H is a microscopic image showing sham mouse superficial skin (top of image) and underlying tumor (bottom of image). Scale bars represent 250 μm.

FIG. 43I is a microscopic image showing treated mouse superficial skin (top of image) and underlying musculature (bottom of image). Scale bars represent 250 μm.

FIG. 44 is a table showing a treatment matrix for mouse tumor ablation.

FIGS. 45A-C are graphs showing finite element modeling using two pulse waveforms which predicts IRE is cell size dependent while BEAM is cell size independent. FIG. 45A: Simulated unipolar 100 μs IRE waveform and bipolar 1 μs BEAM waveform. FIG. 45B: Calculated cellular TMP response for two different cell sizes exposed to an IRE waveform applying 500 V/cm shows TMP size dependence. FIG. 45C: BEAM pulse waveform response shows no TMP cell size dependence at 500 V/cm.

FIGS. 46A-F are diagrams showing finite element models to predict the electric field and thermal distributions within hydrogel platforms. FIG. 46A: Engineered 3D collagen hydrogels are made by adding cell-seeded collagen (0.2% or 2% w/w) into PDMS wells of controlled geometry. They are kept in a well plate under cell culture conditions with nutrients supplied by culture media. FIG. 46B: Mesh used to calculate the electric field distribution within the tissue mimics illustrates the experimental setup for therapy testing. FIGS. 46D-E: Electric field (V/cm) iso-contours when 450 V (FIG. 46C) and 700 V (FIG. 46D) pulses are simulated. FIG. 46E: Temperature isocontours immediately post-therapy (50 pulses of 700 V) show a maximum temperature rise of 12° C. above room temperature. FIG. 46F: Temperature isocontours one minute post-therapy confirm that cells are not exposed to any long-term thermal effects as a result of IRE or BEAM pulses.

FIGS. 47A-C are images and graphs showing ECM-tuned hydrogels which reveal cell size dependent IRE lesions and cell size independent BEAM lesions. FIG. 47A: Altered cell morphology and overall cell size results from changing density of hydrogel matrix from 0.2% to 2.0% collagen (n=25, scale bar 20 μm). FIG. 47B: Comparison of IRE treatment for larger cells in 0.2% collagen reveals larger lesion and thus lower death threshold than for smaller cells in 2% collagen (n=20, p<0.001) (scale bar 1 mm) FIG. 47C: Comparison of BEAM treatment in 0.2% and 2% collagen reveals uniform lesions and thus equivalent death thresholds despite cell size differences. (n=20, p≧0.1) (scale bar 1 mm). (p≦0.0005(***) and p≦0.0001(****)).

FIGS. 48A-C are images and graphs showing constant cell morphology with changing stiffness results in equivalent lethal thresholds for IRE and BEAM. FIG. 48A: Changing the density of alginate does not change cell morphology due to lack of cell-ECM binding sites, allowing for isolating the effect of stiffness on treatments (n=25) FIG. 48B: IRE lesions and lethal thresholds are equivalent across stiffness differences for equivalent cell morphology (n=20, p≧0.1) (scale bar 1 mm) FIG. 48C: BEAM lesions and lethal thresholds are equivalent across alginate stiffness differences (n=20, p≧0.1) (scale bar 1 mm).

FIGS. 49A-F are microscopic images showing histomorphology of normal and neoplastic canine brain tissues ablated with IRE. a) Normal, untreated cerebrocortical grey matter (FIG. 49A) and white matter (FIG. 49C) of the internal capsule. IRE ablation results in neuronal (FIG. 49B) and glial death (FIGS. 49B and D), as well as vacuolization and axonal loss (FIG. 49D). Biopsy of glioblastoma multiforme before (FIG. 49E) and after (FIG. 49F) IRE ablation. The IRE treatment causes disruption of tumor and stromal cytoarchitecture, and tumor cell death. All sections stained with hematoxylin and eosin.

FIG. 50A is a graph showing numerical modeling of the electric field produced by IRE pulses predicts the electric field reaches the cytoplasm inside the cell for only a short duration of the pulse time while the majority of the electric field is retained in the media where it aggregates around the cell membrane.

FIG. 50B is a graph showing numerical modeling of the electric field distribution predicts the electric field produced by BEAM pulses penetrates through the plasma membrane into the cytoplasm for the entire duration of the pulse on-time.

FIG. 50C is a series of fluorescent images of U-87, NHA, C6, and D1TNC1 cells, respectively which allow for determination of shape factors to be used in modeling and to correlate to experimental lesion results.

FIG. 50D is a graph showing U-87, NHA, C6, and D1TNC1 cells show no significant difference (p≧0.1) in overall cell area (n=20).

FIG. 50E is a graph showing nuclear area of malignant glioma cells (U-87 and C6) is greater than for non-malignant astrocytes (NHA and D1TNC1) (n=20, p≦0.05(*) and p≦0.005 (**)).

FIG. 51A is a series of images showing IRE lesion sizes have no significant difference across different cell types (n=10, p≧0.1).

FIG. 51B is a series of images showing BEAM lesion size for malignant glioma cells (U-87 and C6) is greater than non-malignant astrocytes (NHA and D1TNC1) (n=10).

FIG. 51C is a graph showing COMSOL modeling relating lesion size to death thresholds shows no significant difference between IRE thresholds for different cell types (n=10, p≧0.1), confirming the hypothesis that IRE thresholds are primarily dependent on cell size.

FIG. 51D is a graph showing death thresholds for malignant cells are smaller than normal cells with BEAM treatment, which provides that a range of electric field values will kill malignant cells without killing healthy cells (n=10, p≦0.0001 (****)).

FIG. 52A is a series of images showing a cell exposed to IRE treatment shows a diffusion of stained tubulin from the cell cultured in a 3D hydrogel over a 5-minute time course, suggesting a disruption of the outer cell membrane as a result of pulses.

FIG. 52B is a series of images showing a cell exposed to BEAM treatment shows a sharp collapse of the nucleus, and while tubulin staining dims, it does not clearly diffuse outside of original cell membrane area as in the IRE case. This suggests a different effect on both the nucleus and cell between IRE and BEAM.

FIG. 52C is a series of images showing cell not exposed to any pulses acts as a control to ensure no photo-bleaching effects from imaging over 5-minute time course.

FIGS. 53A-53B are graphs showing the predicted TMP and nTMP response to BEAM experimental lethal thresholds for modeled glioma and astrocyte cells suggests a nTMP effect. FIG. 53A: Modeled cells with experimental geometries for glioma cell and astrocytes exposed to simulated BEAM experimental lethal electric field thresholds for the given cell type show a difference in TMP increase in response. FIG. 53B: Modeled cells with experimental geometries for glioma cell and astrocytes exposed to simulated BEAM experimental lethal electric field thresholds for the given cell type show a similar nTMP increase in response, suggesting a value for nTMP increase that will cause cell death.

FIGS. 54A-D are graphs showing applied electric field and TMP for a BEAM treatment (FIGS. 54A-B) and applied electric field and TMP for an IRE treatment (FIGS. 54C-D). In the TMP plots, the dotted line represents a cell with a diameter of 15 um, and the solid line represents a cell with a diameter of 10 um. The maximum TMP across the outer membrane is less dependent on cell size during BEAM than during IRE.

DETAILED DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION

Reference will now be made in detail to various exemplary embodiments of the invention. Embodiments described in the description and shown in the figures are illustrative only and are not intended to limit the scope of the invention. Changes may be made in the specific embodiments described in this specification and accompanying drawings that a person of ordinary skill in the art will recognize are within the scope and spirit of the invention.

Throughout the present teachings, any and all of the features and/or components disclosed or suggested herein, explicitly or implicitly, may be practiced and/or implemented in any combination, whenever and wherever appropriate as understood by one of ordinary skill in the art. The various features and/or components disclosed herein are all illustrative for the underlying concepts, and thus are non-limiting to their actual descriptions. Any means for achieving substantially the same functions are considered as foreseeable alternatives and equivalents, and are thus fully described in writing and fully enabled. The various examples, illustrations, and embodiments described herein are by no means, in any degree or extent, limiting the broadest scopes of the claimed inventions presented herein or in any future applications claiming priority to the instant application.

The present inventors have made the surprising discover that high frequency pulsed electric fields can be manipulated and optimized to target intracellular membranes. More particularly, particular protocols of administering high frequency pulsed electric fields can be used to increase intracellular membrane potentials of the cell in organelles such as the nucleus. By targeting intracellular membrane potentials, cancer cells can be selectively targeted over healthy tissue. In one embodiment, high frequency pulsed electric fields are administered to tumors to create two treatment zones: an ablation zone and a selective therapy zone. In the ablation zone, healthy cells and cancer cells die due to necrotic cell death. Outside the ablation zone, only cancer cells die due to programmed cell death as a result of changes in the membrane potential of intracellular organelles, while healthy cells are spared. Thus, the cell membrane is not the primary target of therapy; resonant additive effects target intracellular components such as the nucleus, mitochondria, and other key membrane-bound organelles. In embodiments, these effects are achieved through an optimization of both pulse length and delay time. In an exemplary embodiment, the pulse length is optimized to be approximately equivalent to the charging time of the cell membrane plus the discharge time of the nuclear envelope, while the delay time is optimized to be approximately equivalent to the charging time of the cell membrane. In embodiments, the delay time is a fraction of the pulse length.

Embodiments of the invention include pulses designed to generate a range of field strengths beyond the tumor margin that results in cell death of aberrant cells while preserving healthy cells. Within the tumor margin, the field strengths are sufficient to kill all cell types. Additionally, embodiments of the invention include pulses designed to generate a range of field strengths beyond the tumor margin that results in enhanced nuclear permeability of aberrant cells while not affecting healthy cells. Within the tumor margin, the field strengths are sufficient to enhance the nuclear permeability of all cell types. Additionally, embodiments of the invention include pulses designed to generate a range of field strengths beyond the tumor margin that slow or arrest the division of aberrant cells while not affecting healthy cells. Within the tumor margin, the field strengths are sufficient to slow the growth rate of all cell types. Additionally, embodiments of the invention include pulses designed to generate a range of field strengths beyond the tumor margin that halts the migration of aberrant cells to prevent metastasis while not affecting healthy cells. Within the tumor margin, the field strengths are sufficient to halt migration of all cell types. Additionally, embodiments of the invention include pulses designed to generate a range of field strengths beyond the tumor margin that prevent the transport of blood and nutrients to aberrant cells. Within the tumor margin, transport of blood and nutrients is prevented to all cell types.

In embodiments, the field strengths generated within the tumor margin are selective to aberrant cells while preserving healthy cells. The electric field waveform may be a rectangular pulse, ramp, decaying exponential, or sine wave and may be unipolar or bipolar. In embodiments, the electric field waveform may be a superimposed, bimodal signal consisting of a low frequency component/harmonic and a high frequency component/harmonic. In embodiments, the electric field waveform may consist of alternating short duration, nanosecond-order pulses with long-duration, microsecond order pulse in succession.

In embodiments, the waveforms are asymmetric to electrophoretically drive exogenous agents, chemical agents, DNA molecules, or nanoparticles through permeabilized membranes. The carrier frequency of the waveforms may be in the range of 100 kHz to 10 MHz. In embodiments, the carrier frequency or pulse duration of the waveforms are chosen based on the cross-over frequency of the cell populations. In other embodiments, the pulses are optimized based on the dielectric properties of the cell populations within the targeted zone of therapy to enable selectivity. In other embodiments, the pulses are optimized based on the physical nucleus to cytoplasm size ratio of the cell populations within the targeted zone of therapy to enable selectivity. In other embodiments, the pulses are designed to generate electro fusion within a select population of cells.

In other embodiments, the pulses are designed to generate simultaneous modulation of the nuclear membrane and outer membrane transmembrane potential. The desired modulatory effect may trigger both reversible electroporation of the nuclear and outer membranes. Alternatively, the desired modulatory effect may trigger reversible electroporation of the outer membrane and irreversible electroporation of the nuclear membrane. Alternatively, the desired modulatory effect triggers both necrosis and apoptosis. Alternatively, the desired modulatory effect slows or arrests cell division. Alternatively, the desired modulatory effect is to prevent metastasis of infiltrative cells.

The treatments may be applied in a single session lasting under 1 hr using an external device. The treatments may be applied over multiple days using an external or implantable device. The resting time between pulses may be varied as part of the optimization routine to select for aberrant cells. The pulses may be delivered in a repetitive manner to lower the required effective field strength and enable the use of solid state switching devices.

In embodiments, the required effective field strength is on the order of 100 to 10,000 V/cm. The solid state switching devices may be arranged in a multi-level, neutral point clamped, or cascaded H-bridge topology.

Embodiments of the invention include an electrical pulse designed to generate a range of field strengths beyond the aberrant cell growth region that results in cell death, slowing the growth rate of, halting the migration of, or preventing the transport of blood and nutrients to aberrant cells while preserving healthy cells, and within the aberrant cell growth region, the field strengths are sufficient to kill, slow the growth rate of, halt migration of, or prevent the transport of blood and nutrients to all cell types. Within the tumor margin, the field strengths are sufficient to enhance the nuclear permeability of all cell types.

Embodiments of the invention include a system for treating a subject suffering from an aberrant cell growth, comprising: at least one electrode configured to be introduced into or adjacent the aberrant cell growth region within the body of a subject, a voltage pulse generator coupled to the electrode and configured to applying multiple electrical pulses to generate an electric field within the growth region with field strengths selective to kill, slow the growth rate of, halt migration of, or preventing the transport of blood and nutrients to aberrant cells while preserving healthy cells.

Embodiments of the invention include a method of treating a subject suffering from an aberrant cell growth, comprising: implanting an electrode into or adjacent the aberrant growth region within the body of a subject, and causing multiple electrical pulses to be emitted from the electrode into the aberrant cell growth region to generate an electric field, wherein the electric field strengths generated within the aberrant cell growth region are selective to kill, slow the growth rate of, halt migration of, or prevent the transport of blood and nutrients to aberrant cells while preserving healthy cells. In embodiments of the method, the electric field has unipolar or bipolar wave form of a rectangular pulse, ramp, decaying exponential, or sine wave. The multiple electrical pulses may take the form of a superimposed, bimodal signal consisting of a low frequency component and a high frequency component. Alternatively, the multiple electrical pulses may consist of alternating short duration, nanosecond-order pulses with long-duration, microsecond order pulse in succession. In embodiments of the method, the frequency of multiple electrical pulses may be in the range of 100 kHz to 10 MHz. In embodiments of the method, the pulses are asymmetric to electrophoretically drive exogenous agents, chemical agents, DNA molecules, or nanoparticles through permeabilized membranes.

In embodiments of the method, the required effective field strength is on the order of 100 to 10,000 V/cm. The carrier frequency or pulse duration of the pulses may be chosen based on the cross-over frequency of the cell populations. Alternatively or additionally, the pulses may be optimized based on the dielectric properties, or the physical nucleus to cytoplasm size ratio of the cell populations within the targeted zone of therapy to enable selectivity. In embodiments of the method, the pulses are designed to generate electro fusion within a select population of cells. In embodiments of the method, the pulses are designed to generate simultaneous modulation of the nuclear membrane and outer membrane transmembrane potential. In embodiments, the desired modulatory effect triggers reversible electroporation of the outer membrane, and irreversible or reversible electroporation of the nuclear membrane. Alternatively or in addition, the desired modulatory effect triggers both necrosis and apoptosis.

In embodiments of the method, the treatments are applied by way of at least one session using an external device or implantable device. The resting time between pulses may be varied as part of the optimization routine to select for aberrant cells. In embodiments, the pulses are delivered in a repetitive manner to lower the required effective field strength and enable the use of solid state switching devices. The solid state switching devices may be arranged in a multi-level, neutral point clamped, or cascaded H-bridge topology.

In embodiments, the pulses, systems, and methods of the invention may have applications in biomedical cancer or tumor treatment.

The following figures further illustrate the invention. FIG. 1 shows an exemplary dual treatment zone of the invention. The white inner portion surrounding the two black circles represents the ablation zone surrounding a pair of electrodes. In the ablation zone both healthy cells and cancers cells undergo necrosis. The orange zone (grey zone, in black and white figures) outside the perimeter of the ablation zone represents the selective therapy zone, in which cancer cells die and healthy cells are spared. The dual treatment zone results from optimized pulse parameters of the invention, which target the membrane potential of intracellular membranes such as the nuclear envelope.

FIG. 2 shows the effects of optimizing pulse parameters on the nuclear transmembrane potential. As can be seen in the figure, a short delay time between bipolar pulses which is a fraction of the pulse length results in an increase in the nuclear transmembrane potential (optimized pulse maximum) that exceeds that of a single pulse (single pulse maximum).

FIG. 3 shows that the nuclear transmembrane potential (nTMP) of cancer cells and healthy cells respond differently to a suboptimal pulse. As shown in the figure, the nuclear transmembrane potential of cancer cells reaches a lethal threshold, while that of a healthy cell is just a fraction of that of a cancer cell. Not wishing to be bound by theory, these differences may be due in part to the larger size of the nucleus in cancer cells. In embodiment, variables were defined as V_(media), V_(cyto), V_(nuc) for the media, cytoplasm, and nucleoplasm domains, respectively. Variables were then defined to calculate the cell membrane (TMP) as (V_(media)−V_(cyto)) and the nuclear membrane (nTMP) a (V_(cyto)−V_(nuc)).

In embodiments, the optimized pulse protocol can be used to increase the transport of molecules between the cytoplasm and intracellular organelles. For example, the optimized pulse protocol of the invention can enhance electro-gene and electro-chemo therapy. Additionally, assymetric pulses can enhance electrophoretic transfer. This is shown schematically in FIG. 4.

In embodiments, bimodal sinusoidal signals can be used to achieve an amplification effect. Indeed, any signal with two or more different frequency components can be used, such as a signal with two, three, four, five, or six frequency components. For example, FIG. 5D shows a bimodal sinusoidal signal comprising two different frequency components, a first frequency component (FIG. 5B) and a higher second frequency component (FIG. 5C); their respective effects on the nuclear transmembrane potential are shown in FIGS. 5E-5G. FIG. 5A is a key to FIGS. 5E-5G which shows how the transmembrane potential of two different cells with different nuclei size are plotted, with the dashed line representing an 8 micrometer diameter cell and the solid line representing a 6 micrometer diameter cell.

Additionally, embodiments of the invention may include one or more systems capable of performing one or more steps of the method. One embodiment of the present invention is illustrated in FIGS. 6 and 7. Representative components that can be used with the present invention can include one or more of those that are illustrated in FIG. 6. For example, in embodiments, one or more probes 22 can be used to deliver therapeutic energy and are powered by a voltage pulse generator 10 that generates high voltage pulses as therapeutic energy, such as pulses capable of irreversibly electroporating the tissue cells of the target tissue. In the embodiment shown, the voltage pulse generator 10 includes six separate receptacles for receiving up to six individual probes 22 which are adapted to be plugged into the respective receptacle. The receptacles are each labeled with a number in consecutive order. In other embodiments, the voltage pulse generator can have any number of receptacles for receiving more or less than six probes.

For example, a treatment protocol according to the invention could include one or more of a plurality of electrodes. According to the desired treatment pattern, the plurality of electrodes can be disposed in various positions relative to one another. In a particular example, a plurality of electrodes can be disposed in a relatively circular pattern with a single electrode disposed in the interior of the circle, such as at approximately the center. Any configuration of electrodes is possible and the arrangement need not be circular but any shape periphery can be used depending on the area to be treated, including any regular or irregular polygon shape, including convex or concave polygon shapes. The single centrally located electrode can be a ground electrode while the other electrodes in the plurality can be energized. Any number of electrodes can be in the plurality such as from about 1 to 20. Indeed, even 3 electrodes can form a plurality of electrodes where one ground electrode is disposed between two electrodes capable of being energized, or 4 electrodes can be disposed in a manner to provide two electrode pairs (each pair comprising one ground and one electrode capable of being energized). During treatment, methods of treating can involve energizing the electrodes in any sequence, such as energizing one or more electrode simultaneously, and/or energizing one or more electrode in a particular sequence, such as sequentially, in an alternating pattern, in a skipping pattern, and/or energizing multiple electrodes but less than all electrodes simultaneously, for example.

In the embodiment shown, each probe 22 includes either a monopolar electrode or bipolar electrodes having two electrodes separated by an insulating sleeve. In one embodiment, if the probe includes a monopolar electrode, the amount of exposure of the active portion of the electrode can be adjusted by retracting or advancing an insulating sleeve relative to the electrode. See, for example, U.S. Pat. No. 7,344,533, which is incorporated by reference herein in its entirety. The pulse generator 10 is connected to a treatment control computer 40 having input devices such as keyboard 12 and a pointing device 14, and an output device such as a display device 11 for viewing an image of a target treatment area such as a lesion 300 surrounded by a safety margin 301. The therapeutic energy delivery device 22 is used to treat a lesion 300 inside a patient 15. An imaging device 30 includes a monitor 31 for viewing the lesion 300 inside the patient 15 in real time. Examples of imaging devices 30 include ultrasonic, CT, MRI and fluoroscopic devices as are known in the art.

The present invention includes computer software (treatment planning module 54) which assists a user to plan for, execute, and review the results of a medical treatment procedure, as will be discussed in more detail below. For example, the treatment planning module 54 assists a user to plan for a medical treatment procedure by enabling a user to more accurately position each of the probes 22 of the therapeutic energy delivery device 20 in relation to the lesion 300 in a way that will generate the most effective treatment zone. The treatment planning module 54 can display the anticipated treatment zone based on the position of the probes and the treatment parameters. Additionally, the treatment planning module 54 may have a user interface which allows a user to input one or more parameters for IRE.

The treatment planning module 54 can display the progress of the treatment in real time and can display the results of the treatment procedure after it is completed. This information can be displayed in a manner such that it can be used for example by a treating physician to determine whether the treatment was successful and/or whether it is necessary or desirable to re-treat the patient.

For purposes of this application, the terms “code”, “software”, “program”, “application”, “software code”, “computer readable code”, “software module”, “module” and “software program” are used interchangeably to mean software instructions that are executable by a processor. The “user” can be any human, including for example, a physician or other medical professional. The treatment planning module 54 executed by a processor outputs various data including text and graphical data to the monitor 11 associated with the generator 10.

Referring now to FIG. 7, the treatment control computer 40 of the present invention manages planning of treatment for a patient. The computer 40 is connected to the communication link 52 through an I/O interface 42 such as a USB (universal serial bus) interface, which receives information from and sends information over the communication link 52 to the voltage generator 10. The computer 40 includes memory storage 44 such as RAM, processor (CPU) 46, program storage 48 such as ROM or EEPROM, and data storage 50 such as a hard disk, all commonly connected to each other through a bus 53. The program storage 48 stores, among others, a treatment planning module 54 which includes a user interface module that interacts with the user in planning for, executing and reviewing the result of a treatment. Any of the software program modules in the program storage 48 and data from the data storage 50 can be transferred to the memory 44 as needed and is executed by the CPU 46.

In embodiments, the user interface may be a graphical user interface which may be used in conjunction with the computer readable code. The user interface may allow a user to enter or input one or more parameters to be used by the treatment planning module 54 in setting a treatment protocol for IRE. The user interface may allow such input through the use of text fields, check boxes, pull-downs, sliders, command buttons, and the like. Based on this input 54, the treatment planning module 54 can calculate a threshold electric field for IRE of the target tissue and one or more parameters of a treatment protocol for administering the IRE in a manner sufficient to produce this threshold electric field.

In embodiments, the treatment planning module 54 provides for numerical modeling capabilities such as those described in the Examples. The model may be used to simulate the nuclear and cellular transmembrane potential of various pulsing parameters prior to treatment. A user interface may allow input of one or more of the parameters listed in the table in FIG. 10 as well as values for pulse length, interpulse delay, electric field strength, etc., and from these a graphic representation of the nuclear and cellular transmembrane potential may be plotted. Additionally, the treatment planning module may allow for a visualization of an ablation zone and surrounding selective treatment zone on the display device 11 based on input of one or more of the parameters.

In one embodiment, the computer 40 is built into the voltage generator 10. In another embodiment, the computer 40 is a separate unit which is connected to the voltage generator through the communications link 52. In a preferred embodiment, the communication link 52 is a USB link. In one embodiment, the imaging device 30 is a standalone device which is not connected to the computer 40. In the embodiment as shown in FIG. 6, the computer 40 is connected to the imaging device 30 through a communications link 53. As shown, the communication link 53 is a USB link. In this embodiment, the computer can determine the size and orientation of the lesion 300 by analyzing the data such as the image data received from the imaging device 30, and the computer 40 can display this information on the monitor 11. In this embodiment, the lesion image generated by the imaging device 30 can be directly displayed on the grid (not shown) of the display device (monitor) 11 of the computer running the treatment planning module 54. This embodiment would provide an accurate representation of the lesion image on the grid, and may eliminate the step of manually inputting the dimensions of the lesion in order to create the lesion image on the grid. This embodiment would also be useful to provide an accurate representation of the lesion image if the lesion has an irregular shape.

It should be noted that the software can be used independently of the pulse generator 10. The user can plan the treatment on a different computer as will be explained below and then save the treatment parameters to an external memory device, such as a USB flash drive (not shown). Any non-transitory computer-readable media can be used to store the software and/or the output of the software for a particular treatment protocol. The data from the memory device relating to the treatment parameters can then be downloaded onto the computer 40 to be used with the generator 10 for treatment. Additionally, the software can be used for hypothetical illustration of zones of ablation, temperature thresholds or cutoffs, and electrical field thresholds or cutoffs for training purposes to the user on therapies that deliver electrical energy. For example, the data can be evaluated by a human to determine or estimate favorable treatment protocols for a particular patient rather than programmed into a device for implementing the particular protocol. The treatment protocols can be designed to produce the minimum electrical field threshold for inducing IRE calculated by the treatment planning module 54.

FIG. 8 illustrates one embodiment of a circuitry to detect an abnormality in the applied pulses such as a high current, low current, high voltage or low voltage condition. This circuitry is located within the generator 10 (see FIG. 6). A USB connection 52 carries instructions from the user computer 40 to a controller 71. The controller can be a computer similar to the computer 40 as shown in FIG. 2. The controller 71 can include a processor, ASIC (application-specific integrated circuit), microcontroller or wired logic. The controller 71 then sends the instructions to a pulse generation circuit 72. The pulse generation circuit 72 generates the pulses and sends electrical energy to the probes. For clarity, only one pair of probes/electrodes is shown. However, the generator 10 can accommodate any number of probes/electrodes (e.g., from 1-10, such as 6 probes) and energizing multiple electrodes simultaneously for customizing the shape of the ablation zone. In the embodiment shown, the pulses are applied one pair of electrodes at a time, and then switched to another pair. The pulse generation circuit 72 includes a switch, preferably an electronic switch that switches the probe pairs based on the instructions received from the computer 40. A sensor 73 such as a sensor can sense the current or voltage between each pair of the probes in real time and communicate such information to the controller 71, which in turn, communicates the information to the computer 40. If the sensor 73 detects an abnormal condition during treatment such as a high current or low current condition, then it will communicate with the controller 71 and the computer 40 which may cause the controller to send a signal to the pulse generation circuit 72 to discontinue the pulses for that particular pair of probes. The treatment planning module 54 can further include a feature that tracks the treatment progress and provides the user with an option to automatically retreat for low or missing pulses, or over-current pulses (see discussion below). Also, if the generator stops prematurely for any reason, the treatment planning module 54 can restart at the same point where it terminated, and administer the missing treatment pulses as part of the same treatment. In other embodiments, the treatment planning module 54 is able to detect certain errors during treatment, which include, but are not limited to, “charge failure”, “hardware failure”, “high current failure”, and “low current failure”.

General treatment protocols for the destruction (ablation) of undesirable tissue through electroporation are known. They involve the insertion (bringing) electroporation electrodes to the vicinity of the undesirable tissue and in good electrical contact with the tissue and the application of electrical pulses that cause irreversible electroporation of the cells throughout a region of or the entire area of the undesirable tissue. The cells whose membrane was irreversible permeabilized may be removed or left in situ (not removed) and as such may be gradually removed by the body's immune system. Cell death is produced by inducing the electrical parameters of irreversible electroporation in the undesirable area.

Electroporation protocols involve the generation of electrical fields in tissue and are affected by the Joule heating of the electrical pulses. When designing tissue electroporation protocols it is important to determine the appropriate electrical parameters that will maximize tissue permeabilization without inducing deleterious thermal effects. It has been shown that substantial volumes of tissue can be electroporated with reversible electroporation without inducing damaging thermal effects to cells and these volumes have been quantified (Davalos, R. V., B. Rubinsky, and L. M. Mir, Theoretical analysis of the thermal effects during in vivo tissue electroporation. Bioelectrochemistry, 2003. Vol. 61(1-2): p. 99-107).

The electrical pulses used to induce irreversible electroporation in tissue are typically larger in magnitude and duration from the electrical pulses required for reversible electroporation. Further, the duration and strength of the pulses for irreversible electroporation are different from other methodologies using electrical pulses such as for intracellular electro-manipulation or thermal ablation. The methods are very different even when the intracellular (nano-seconds) electro-manipulation is used to cause cell death, e.g. ablate the tissue of a tumor or when the thermal effects produce damage to cells causing cell death.

Typical values for pulse length for irreversible electroporation are in a range of from about 5 microseconds to about 62,000 milliseconds or about 75 microseconds to about 20,000 milliseconds or about 100 microseconds±10 microseconds. This is significantly longer than the pulse length generally used in intracellular (nano-seconds) electro-manipulation which is 1 microsecond or less—see U.S. Published Patent Application No. 2002/0010491.

The pulse is typically administered at voltage such that the local electric field experienced by the tissue is about 100 V/cm to 7,000 V/cm or 200 V/cm to 2000 V/cm or 300V/cm to 1000 V/cm about 600 V/cm for irreversible electroporation. This is substantially lower than that used for intracellular electro-manipulation which is about 10,000 V/cm—see U.S. Published Patent Application No. 2002/0010491.

The voltage expressed above is the voltage gradient (voltage per centimeter). The electrodes may be different shapes and sizes and may be positioned at different distances from each other. The shape may be circular, oval, square, rectangular or irregular etc. The distance of one electrode to another may be in the range of about 0.5 to 10 cm, 1 to 5 cm, or 2-3 cm, for example. The electrode may have a surface area of 0.1-5 sq. cm or 1-2 sq. cm, for example.

The size, shape and distances of the electrodes can vary and such can change the voltage and pulse duration used. Those skilled in the art will adjust the parameters in accordance with this disclosure to obtain the desired degree of electroporation and avoid thermal damage to surrounding cells.

A primary factor in determining the effect of an electroporation procedure is the electric field to which the tissue is exposed. However, IRE protocols have a variety of electrical pulse parameters that may also affect the toxicity of the treatment. In addition to the electric field, these include pulse shape, number of pulses, pulse length, and repetition rate. The thermal effects of an IRE treatment during a pulse are a direct function of the conductivity of the tissue and the voltage to which it is exposed. Therefore, minimizing the thermal effects for a particular tissue type may be done by finding the minimum required electric field, and thus applied voltage, to kill the cells in the tissue.

To this end, pulse parameters and electrode configurations according to embodiments of the invention can include any combination of any of the following: a pulse length in the range of about 1 μs to 1 ms; a number of pulses ranging from 1 to 10,000; an electric field distribution for each conductive wire pair and/or across a treatment region ranging from about 5-5,000 V/cm; a total electrical charge delivered by way of each conductive wire pair and/or across a treatment region of about 0.1 to about 500 mC; a frequency of pulse application ranging from about 0.001-100 Hz; a frequency of pulse signal ranging from about 0-100 MHz; a pulse shape that is square, exponential decay, sawtooth, sinusoidal, or of alternating polarity although the currently favored pulse shape is a biphasic DC pulse; a positive, negative, and neutral electrical charge pulses (changing polarity within the pulse); a resulting current in the treated tissue ranging from about 0 to about 100 amps; from 1-20 electrodes and/or electrically conductive wires; an electrode and/or electrically conductive wire separation distance ranging from about 0.1 mm to about 5 cm; and multiple sets of pulse/electrode parameters for a single treatment, including changing any of the above parameters within the same treatment, such as removing the electrodes and replacing them in different locations within the tissue or changing the number of electrodes, to specialize/customize outcome.

In embodiments treatment protocols can employ a pulse length in the range of about 250 ns and 50 μs, with a delay between pulses on that order. Pulse lengths ranging from about 1 μs to 1 ms are also possible, such as from about 5 μs to about 0.5 ms, or from about 10 μs to about 0.1 ms, or from about 15 μs to about 95 μs. Pulse lengths of 20 μs, 25 μs, 30 μs, 35 μs, 40 μs, 45 μs, 50 μs, 55 μs, 60 μs, 65 μs, 70 μs, 75 μs, 80 μs, 85 μs, 90 μs, 110 μs, 150 μs, or 200 μs, and so on are also acceptable. In some embodiments, the pulse duration of the electroporation-based therapy can exceed 100 μs. Any length pulse or pulse train can be administered in embodiments according to the invention. For example, pulse lengths of about 1 picosecond to 100 seconds can be used, such as from 10 picoseconds to about 10 seconds, or for example from about 100 picoseconds to about 1 second, or from 1 nanosecond to 100 milliseconds, or from about 10 nanoseconds to about 10 milliseconds, or from about 100 nanoseconds to about 1 millisecond, or from about 1 microsecond or 10 microseconds to about 100 microseconds. Some embodiments may have a pulse length ranging from about 100 microseconds to about 1 second, such as a pulse length of about 110, or 120, or 130, or 140, or 150, or 200, or 300, or 350, or 400, or 500, or 600, or 700, or 800 or 900 microseconds, or about 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 milliseconds, or even 15, 20, 30, 40, 50, 60, 70, 80, 90, or 100 milliseconds, or even for example from about 200, 300, 400, 500, 600, 700, 800, or 900 milliseconds and so on.

In exemplary embodiments, the pulses are monopolar or bipolar and the pulse length may range from about 0.25 microseconds to about 100 microseconds, including 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, and 90 μs, or any range in between these values.

In exemplary embodiments, successive pulses, whether monopolar or bipolar may have an interpulse delay between about 0.1 microseconds to about 200 microseconds, including 0.2 microseconds, 0.3 microseconds, 0.4 microseconds, 0.5 microseconds, 0.6 microseconds, 0.7 microseconds, 0.8 microseconds, 0.9 microseconds, 1 microsecond, 1.5 microseconds, 2 microseconds, 2.5 microseconds, 3 microsecond, 3.5 microseconds, 4 microseconds, 4.5 microseconds, 5 microseconds, 5.5 microseconds, 6 microseconds, 6.5 microseconds, 7 microseconds, 7.5 microseconds, 8 microseconds, 8.5 microseconds, 9 microseconds, 9.5 microseconds, 10 microseconds, 20 microseconds, 30 microseconds, 40 microseconds, 50 microseconds, 60 microseconds, 70 microseconds, 80 microseconds, 90 microseconds, 100 microseconds, 120 microseconds, 140 microseconds, 160 microseconds, and 180 microseconds, or any range in between these values.

In exemplary embodiments, the interpulse delay is a portion of the pulse length, including 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, and 95% of the pulse length, or any range in between these values. In exemplary embodiments, the interpulse delay exceeds the pulse length, including 1.1×, 1.2×, 1.3×, 1.4×, 1.5×, 1.6×, 1.7×, 1.8×, 1.9×, 2.0×, 2.2×, 2.4×, 2.6×, 2.8×, 3.0×, 3.2×, 3.4×, 3.6×, 3.8×, 4.0×, 4.2×, 4.4×, 4.6×, 4.8×, 5.0×, 5.5×, 6.0×, 6.5×, 7.0×, 7.5×, 8.5×, 9.0×, 9.5×, and 10.0× the pulse length, or any range in between these values.

The number of pulses can range for example from 5 to 5,000, or from about 10 to 2,000, or from about 20 to 1,000, or from about 30 to 500, or from about 50 to 200, or from about 75 to 150, or from about 90 to 120, or from about 95 to 110, or about 100 pulses. According to other embodiments, the number of pulses can range from about 5 to about 400 pulses, such as from about 10 to about 350 pulses, or for example from about 15 to about 300 pulses, including from about 20 to about 250 pulses, or from about 25 to about 200 pulses, such as from about 30 to about 150 pulses, for example from about 50 to about 125 pulses, such as from about 75 to about 175 pulses, or from about 90 to 110 pulses, such as about 100 pulses.

Typically, the electric field distribution for each conductive wire pair and/or across a treatment region for IRE is performed using voltages ranging for example between 1500 V/cm to 4,000 V/cm, including 1500 V/cm to 2000 V/cm, 2000 V/cm to 3000 V/cm, 3000 V/cm to 4000 V/cm, 2000 V/cm to 4000 V/cm, 2500 V/cm to 4000 V/cm, and so on. Voltages of much lower power can also be used, including using less than about 1500 V/cm. Applied fields of about 500 V/cm to 1000 V/cm can be used, or even of about 10 V/cm to about 750 V/cm, such as from about 50 V/cm to about 200 V/cm, or an electric field distribution of about 75 V/cm to about 100 V/cm. For example, in the treatment of brain tumors, typically, an applied field of less than 1000 V/cm can be used. Electrical pulse generators that can be used include those capable of delivering from 0 to about 5,000 V, such as the NanoKnife® system of AngioDynamics®, which for example can deliver from 0-3,000 V.

In another embodiment, the amplitude of the pulses of the electroporation-based therapy exceeds 2000 V/cm, including an amplitude of about 2200 V/cm, or 2500 V/cm, such as about 3000 V/cm, or 3500 V/cm, or about 4000 V/cm, such as 4500 V/cm, or about 5000 V/cm, such as about 5500 V/cm, or about 6000 V/cm, or about 6500 V/cm, such as about 7000 V/cm, or about 7500 V/cm, such as 8000 V/cm, or about 8500 V/cm, including 9000 V/cm, or about 9500 V/cm, such as about 10,000 V/cm and so on. Amplitude in the context of this specification refers to the magnitude of the electrical energy being applied using electrical pulses and which pulses can be of either positive or negative polarity.

According to methods of the invention, cycle times for pulses are set generally about 1 Hz. Furthermore, it has been found that alternating polarity of adjacent electrodes minimizes charge build up and provides a more uniform treatment zone. More specifically, in experiments performed by the inventors, a superficial focal ablative IRE lesion was created in the cranial aspect of the temporal lobe (ectosylvian gyms) using the NanoKnife® (Angiodynamics, Queensbury, N.Y.) generator, blunt tip bipolar electrode (Angiodynamics, No. 204002XX) by delivering 9 sets of ten 50 μs pulses (voltage-to-distance ratio 2000 V/cm) with alternating polarity between the sets to prevent charge build-up on the stainless steel electrode surfaces. These parameters were determined from ex-vivo experiments on canine brain and they ensured that the charge delivered during the procedure was lower than the charge delivered to the human brain during electroconvulsive therapy (an FDA approved treatment for major depression). Excessive charge delivery to the brain can induce memory loss, and thus is preferably avoided.

Specific method embodiments may employ administering electroporation based therapy using a pulse rate of about 1 Hz to 20 GHz, such as for example from about 10 Hz to 20 GHz, or about 50 Hz to 500 Hz, or 100 Hz to 1 kHz, or 10 kHz to 100 kHz, or from 250 kHz to 10 MHz, or 500 kHz to 1 MHz, such as from 900 kHz to 2 MHz, or from about 100 MHz to about 10 GHz, including from about 200 MHz to about 15 GHz and so on. In an exemplary embodiment, the pulse rate is between 100 kHz and 10 MHz.

In preferred embodiments, a total electrical charge delivered by way of each conductive wire pair and/or across a treatment region of about 0.5 to about 25 mC can be used, such as about 1 mC to about 20 mC, or from about 1.5 mC to about 15 mC, or from about 2 mC to about 10 mC, or from about 5 mC to about 8 mC, and so on. Similarly, in preferred embodiments, the resulting current in the treated tissue can range for example from about 1 A to about 8 A, or from about 2 A to about 6 A, or from about 3 A to about 5 A, such as 4 A. Indeed, for certain applications the total electrical charge delivered can range from about 0.5 to about 500 mC, such as about 10 mC to about 200 mC, or from about 15 mC to about 150 mC, or from about 20 mC to about 100 mC, or from about 50 mC to about 80 mC, and so on. The resulting current in the treated tissue can range for example from about 1 A to about 80 A, or from about 20 A to about 60 A, or from about 30 A to about 50 A, such as 40 A. It is not uncommon for currents for IRE treatments to reach or exceed 40 and 50 amps, and it is further feasible to operate under even higher current with pulse generators capable of operating under such conditions as well. Currents are expected to be high in certain applications, especially when working in an area where the tissue or the medium is highly conductive, such as with blood present in a blood vessel. Pulse width, pulse shape, number of pulses, and the resultant current in the tissue can be adjusted to achieve specific target goals for limiting the total electric charge, and any of the specific values disclosed in this specification can be used to calculate the target expected charge.

Any number of electrically conductive wires or electrodes can also be used. However, in preferred embodiments 3 to about 18 electrodes are used, such as 3 to 16, or from about 3 to 15, or from 4 to 12, or from 5 to 10, or from 6 to 8. Any one or more of the electrodes/wires can be selectively energized to achieve a particular treatment result. Further, the separation distance between electrically conductive surfaces, such as electrically conductive wires and/or electrodes, can range from about 0.2 mm to about 4 mm, such as ranging from about 0.3 mm to about 3 mm, or from about 0.4 mm to about 2 mm, or from about 0.5 mm to about 1 mm, or from about 0.8 mm to about 4 cm, such as from about 0.9 mm to about 3 cm, or from about 1.2 cm to about 2 cm, or from about 1.5 cm to about 1.8 cm, and so on.

Additional parameters of protocols that can be used in embodiments of the invention are provided in U.S. Published Patent Application Nos. US 2007/0043345, 2009/0269317, 2011/0106221, 2012/0109122, 2013/0184702, 2013/0345697, 2014/0039489, and 2015/0088120, as well as in U.S. Pat. Nos. 8,926,606, 8,992,517, 8,814,860, 8,465484, the disclosures of each of which are hereby incorporated by reference in their entireties.

EXAMPLES

The following Examples serve to further illustrate the invention.

Example 1 presents a bimodal enhanced ablation mechanism (BEAM) platform that uses one or more bursts of high frequency electric fields which have been specifically optimized to modulate intracellular effects in cancer cells while sparing healthy tissue. An optimal burst contains constitutive pulses with durations approximately equivalent to the charging time of the cell membrane plus the discharge time of the nuclear envelope. This novel concept is expanded upon further in the following sections and has implications for targeting specific cancer types without the need of external markers but with similar specificity to pharmaceutical compounds.

Example 2 presents the in-vitro effects of high frequency bi-polar bursts. Individual pulses within the burst are separated by 2 μs and sequential pulses alternate in polarity. The bursts are repeated once per second for 80 seconds and each burst exposes cells to the applied voltages for 100 μs. To demonstrate the effects of these pulses on the cell membrane and intracellular organelles, the inventors present a finite element model of a cell including a nuclear envelope. The charging behavior of the lipid-bilayer and nuclear envelope is evaluated in response to pulses between 250 ns and 50 μs. A parametric analysis is conducted on the intra- and extracellular conductivity, nucleus-to-cytoplasm ratio, and pulse-to-pulse delay time. In-vitro experiments are presented to confirm the non-thermal nature of the protocol and demonstrate irreversible electroporation within this intermediate pulse-width range.

In Example 3, the inventors explored the pulse-duration space between 250 ns and 100 μs and calculated the lethal electric field intensity for specific bimodal enhanced ablation mechanism (BEAM) protocols using a 3D tumor mimic. The inventors found that the nominal lethal thresholds for bursts containing 0.25, 0.5, 1, 2, 5, 10, and 50 μs pulses were 2022, 1687, 1070, 755, 640, 629, and 531 V/cm, respectively. A murine tumor model was used to investigate the effectiveness of BEAM in vivo. Tumors were exposed to 200 bursts, each energized for 100 μs, containing individual pulses 1, 2, or 5 μs in duration. In all treatment groups, average tumor growth was substantially inhibited versus control. 6 of 14 treated mice had no measurable signs of tumors 30 days after treatment and all protocols were able to achieve complete regressions. This work shows the potential for BEAM to be used as a focal therapy and merits its investigation in larger pre-clinical models.

In Example 4, the inventors report a physical treatment method based on electrical disruption of cells, whose action depends strongly on cellular morphology. Interestingly, numerical modeling suggests that while outer lipid bilayer disruption induced by long pulses (˜100 μs) is enhanced for larger cells, short pulses (˜1 μs) preferentially result in high fields within the cell interior, which scale in magnitude with nucleus size. Because enlarged nuclei represent a reliable indicator of malignancy, this presents one method for preferentially targeting malignant cells. While the inventors demonstrate killing of both normal and malignant cells using pulsed electric fields (PEFs) to treat spontaneous canine GBM, properly tuned PEFs can be used to provide targeted ablation based on nuclear size. Using 3D hydrogel models of normal and malignant brain tissues, which permit high-resolution interrogation during treatment testing, the inventors confirmed that PEFs could be tuned to preferentially kill cancerous cells. Finally, the inventors estimated the nuclear envelope electric potential disruption needed for cell death from PEFs. The results may be useful in safely targeting the therapy-resistant cell niches that cause recurrence of GBM tumors.

Example 1

A numerical model of a cell in suspension was created in Comsol 4.2a. Two schemes were used to model the cell as a membrane covered sphere. In the first model, individual domains were created representing the sample fluid (external to cell), cell membrane, and cytoplasm (internal to cell). The 5 nm thick spherical shell domain representing the cell membrane required significant modification to the default meshing parameters and resulted in a large number of tetrahedral elements. Briefly, the entire geometry was assigned a single mesh with a predefined density of ‘Extremely course’. The values for the default parameters were then changed for minimum element size (0.00025), maximum element growth rate (1.2), resolution of curvature (0.04), and resolution of narrow regions (0.0001) to successfully mesh the geometry with 817,184 tetrahedral elements. A computer with a quad core 3.0 GHz processor and 8 GB of ram required 15 hours of computation time to solve a 14 μs transient model with 1,092,902 degrees of freedom (results shown in FIG. 9). This model was presumably the most accurate approach and was used to calculate the frequency, sinusoidal, and pulse response of the TMP for conductivities between 0.01 and 10 S/m. However, it was computationally expensive and limited analysis of transmembrane potentials to the outer cell membrane.

To model the effects of bursts of bipolar square waves and effects on the nuclear membrane, a more efficient impedance boundary condition model was used. In this method, a cubic domain represented the experimental media and two spheres represented the domains for the cytoplasm and nucleoplasm, respectively. For each domain, a separate Electric Currents physics module was used and the dependent voltage variables were defined as V_(media), V_(cyto), V_(nuc) for the media, cytoplasm, and nucleoplasm domains, respectively. Variables were then defined to calculate the cell membrane (TMP) and nuclear membrane (nTMP) as (V_(media)−V_(cyto)) and (V_(cyto)−V_(nuc)), respectively. In the Electric Currents module, the boundaries representing membranes were defined as impedance boundary conditions with reference voltages prescribed as the voltage in the adjacent domain. In the Media domain, the boundary representing the cell membrane was defined as an impedance boundary with reference voltage of V_(cyto). The layer specification was defined as a ‘thin layer’ and the electrical conductivity, relative permittivity, and surface thickness were defined using the values presented in the table in FIG. 10.

In the impedance boundary condition model, the mesh was defined as a single Free Tetrahedral group with ‘Normal’ sized elements resulting in 17,825 tetrahedral elements. In a preliminary study of this model, an additional mesh refinement step (Number of refinements=2) was also taken. With refinement, this computation of the same 14 μs simulation was completed in 27 minutes. Without refinement, the computation time was further reduced to 14 minutes. When compared to the physical boundary model, both impedance boundary configurations sufficiently reproduced similar results. The unrefined impedance boundary condition model was used to conduct the remaining parametric studies.

Analytical Modeling

In order to investigate the effects of a bi-modal sine wave on electroporation, an analytical model was implemented that solved the Laplace equation in the frequency domain for a spherical cell with a concentric nucleus (Yao, C. G., et al., Study of transmembrane potentials of inner and outer membranes induced by pulsed-electric-field model and simulation. IEEE Trans Plasma Sci, 2007. 35(5): p. 1541-1549). Each cellular region was characterized by both a dielectric permittivity and conductivity, ensuring TMP and nTMP computational accuracy with frequencies is the MHz range. Briefly, solutions were obtained by merging a low-frequency (250 kHz) and high-frequency (1 MHz) electric field in the time domain, converting the signal to the frequency domain by taking the Laplace Transform, multiplying the signal by a transfer function representing the geometric and dielectric properties of the cell (Kotnik, T. and D. Miklavcic, Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields. Biophysical Journal, 2006. 90(2): p. 480-491), and converting the result back to the time domain by taking the inverse Laplace transform. To illustrate the clinical benefits of the optimized burst, the Laplace equation was solved for two needle electrodes (Ø 1 mm) in an infinite tissue domain according to standard techniques. The electrodes were spaced 0.1 cm apart and the applied voltage was set to 20 kV.

Cell Preparation and Experimentation

MDA-MB-231 human breast cancer cells were suspended in buffer with conductivity of 0.1 S/m at a concentration of 2.5×10⁶ cells/ml. A custom pulse generation system capable of delivering 1000 V_(Peak) in each polarity was used to create electric field intensities of approximately 1000, 2000, and 4000 V/cm across cell suspensions in 1 mm or 2 mm electroporation cuvettes. MDA-MB-231 cells were exposed to 90 bursts consisting of 200 bipolar square wave pulses 700 ns wide separated by 1.8 μs of dead time, shown in FIG. 14 (top and middle) at a repetition rate of 1 Hz. Cell viability was assessed 1 and 16 hours post treatment using a Vi-Cell cell viability analyzer (Beckman Coulter). Total viability after 16 hours was quantified as the ratio of live treated cells to live untreated (sham control) cells.

Additional experiments were conducted with PPT8182 murine primary pancreatic tumor cells suspended in a buffer at a concentration of 5×10⁶ cells/ml with a media conductivity of 0.2 S/m. 100 μL of cell suspension were added to a 2 mm gap cuvette and 80 bursts with 50 microseconds on time in each polarity (100 μs total) were applied. Within each burst, individual pulses had on times of 250 ns, 500 ns, 1 μs, 2 μs, 5 μs, 10 μs, or 50 μs with a 2 μs delay between the end of a pulse and the beginning of the next pulse in the opposite polarity. The cells were exposed to electric fields with magnitudes of 1500 V/cm, 3000 V/cm, and 4000 V/cm.

Numerical Modeling (Outer Membrane)

FIG. 11 shows the maximum TMP for an MDA-MB-231 cell in a 400 V/cm electric field for frequencies between 1 Hz and 100 MHz. DC and low frequency sinusoidal voltages are very effective at increasing the TMP of the cell membrane due to the averaged energized time being much longer than the charging time of the cell membrane. As a result, for a low frequency sinusoidal voltage of 400 V/cm, the TMP is elevated and held at a value greater than the threshold for electroporation independent of the conductivity of the media. In low conductivity solutions, the cell membrane charges more slowly. As the frequency is increased above 1 kHz, the voltage is not on for long enough to fully charge the cell membrane in 0.01 S/m buffer. The results show that the optimal frequency range for interacting with cells without significantly altering their cell membrane occurs above 1 kHz. When operating above 100 kHz, very large magnitude electric fields can be used without significantly increasing the TMP.

Interestingly, previous experimental observations (Sano, M., J. Caldwell, and R. Davalos, A Low Frequency Contactless Dielectrophoresis Platform for Particle Isolation and Enrichment. 2011: USA; Sano, M. B., J. L. Caldwell, and R. V. Davalos, Modeling and Development of a Low Frequency Contactless Dielectrophoresis (cDEP) Platform to Sort Cancer Cells from Dilute Whole Blood Samples. Biosensors & Bioelectronics, 2011; and Sano, M. B., et al., Contactless Dielectrophoretic Spectroscopy: Examination of the Dielectric Properties of Cells Found in Blood. Electrophoresis, 2011. DOI 10.1002/elps.2201100351) showed some degree of electroporation of cells below the first crossover frequency of their Clausius-Mossotti factor, but minimal electroporation above this frequency (i.e. cells were electroporated while experiencing negative DEP, but minimally impacted when experiencing positive DEP). Analysis of the results shown in FIG. 11 shows that the cross-over frequency is collocated with the −3 dB point on the TMP curve. This indicates that at the cross-over frequency, cells are absorbing approximately half of the maximum energy absorbed at lower frequencies and shows the strong dependence of membrane electrical characteristics on DEP and Electroporation effects.

As the conductivity of the media is increased, the charging time of the cell membrane decreases until the media conductivity reaches 1.0 S/m. Above this threshold, increases in media conductivity negligibly impact the TMP charging time. At 0.1 S/m, the −3 dB frequency is not reached until approximately 100 kHz. At 1.0 and 10.0 S/m, this frequency is shifted higher to approximately 300 kHz. If higher conductivity buffers are used in in-vitro experiments, then the frequency range should also be shifted to avoid damaging cell membranes.

FIGS. 12A and 12B shows the time dependent charging of the TMP for a 1000 V/cm electric field at frequencies of 100 kHz and 1 MHz, respectively. At 100 kHz, the maximum TMP is negligibly affected by media conductivity. At 0.01 S/m there is a slight phase shift and decrease in the maximum value achieved. At 1 MHz, the TMP is drastically affected by media conductivity. A phase shift and decrease is evident for 0.01 and 0.1 S/m conductivity media. This again indicates that low conductivity media provide some measure of protection to cells against lipid bilayer electroporation. In media with conductivity above physiological norms (1.0 S/m), the TMP increases significantly (and in phase) with the applied signal.

FIGS. 13 and 14 show the TMP response to 2 and 20 μs pulsed electric fields with 1000 V/cm magnitudes, respectively. As anticipated from the results with sinusoidal signals, the rate of TMP increase is highly dependent on media conductivity. For the lowest media conductivity (0.01 S/m), it takes longer than 20 μs for the TMP to reach its maximum value. This charging time reduces to approximately 2 μs for conductivities of 1.0 S/m or greater. These results show the exponential increase and decrease in TMP caused by pulsed electric fields. The slower charging rate in physiological conductivities is due to a preference for currents to flow through the cell rather than around it. This highlights the ability to optimize pulse parameters to preferentially impact intracellular components.

Numerical Modeling (Nuclear Membrane)

When a cell is exposed to a pulsed electric field, the capacitive nature of the cell membrane blocks the flow of current through the cell when fully charged. However, the membrane cannot charge instantaneously and there is a brief time when ions and molecules are rearranging and current flows through the cytoplasm of the cell. This displacement current increases the transmembrane potential of membranes surrounding the nucleus and organelles. These cellular components are much smaller than the cell and their theoretical maximum TMP within the same electric filed decreases linearly with their effective radius. Additionally, as a fully charged cell membrane blocks the flow of current through the cytoplasm, these internal membranes can charge for a period less than the TMP charging time.

FIG. 15 shows the charging characteristics of the cell and nuclear membranes for a bipolar pulse with 4 μs on- and 2 μs off-times. For the first 500 ns, current flows through the cytoplasm and the nuclear transmembrane potential (nTMP) increases. After 500 ns, the cell membrane begins to block the flow of current and the nTMP begins to decay back to zero. As the positive going pulse turns off, the charge on the cell membrane begins to dissipate and ions redistributing cause a current to flow in the opposite direction, charging the nuclear membrane in the opposite polarity. This process repeats as the pulse switches polarity. Every bi-polar pulse results in four increases in nTMP with pattern++−−++. This pattern of successive nTMP increase in the same polarity suggests that there exists an optimal pulse configuration to increase the maximum nTMP value achievable.

FIG. 16 shows the impact of pulse on time on the nTMP when the pulse off time is held constant at 500 ns. At the onset of the first positive pulse, the nTMP charges up to a maximum of approximately 0.35 V in the first 500 ns before it starts to decay. At the end of the first pulse, displacement currents within the cytoplasm force the nTMP negative. The onset of the negative polarity pulse further increases the magnitude of the nTMP in the negative direction. This additive effect results in a negative nTMP value which is greater in magnitude than the first positive nTMP.

For very short on-time pulses, the nuclear membrane has not fully discharged before the positive pulse returns to zero. This diminishes the maximum negative nTMP achievable. For 500 ns on time pulses, the first positive nTMP reaches 0.35 V while the first negative nTMP reaches −0.47 V. This effect is further enhanced if the positive nTMP is given sufficient time to decay back to zero before the positive pulse is turned off. When the pulse length is increased to 3.5 and 4 μs, the nTMP reaches a maximum magnitude of 0.62 V, nearly double the value achieved by a single mono-polar pulse. FIG. 16 shows the nuclear transmembrane potential can be doubled without increasing the magnitude of the applied field by carefully tuning the pulse parameters.

FIG. 17 shows the effect of delay time between pulses. At the end of the first positive pulse, the nTMP decays and becomes negative after approximately 250 ns. It reaches its maximum negative value approximately 500 ns after the end of the first positive pulse before decaying back towards zero. If the negative pulse is initiated before the nTMP can decay back to zero, then the resulting increase in nTMP is greater than that achieved by a single mono-polar pulse. The maximum nTMP value is achieved when the delay between pulses is 500 ns. This optimum time is due to a combination of factors that contribute to the RC time constants for the cell and nuclear membranes. The results shown in FIGS. 16 and 17 show that the pulse characteristics can be optimized to increase the maximum nTMP achievable for high frequency bipolar pulses.

It appears that to maximize the nTMP, the optimal pulse on time is equivalent to the charging time of the cell membrane plus the discharge time of the nuclear membrane. This allows the nTMP to charge up, then return to zero before it is forced negative at the falling edge of the pulse. Similarly, the optimal off time is approximately equivalent to the charging time of the cell membrane. This allows the nTMP to be increased to its maximum opposite polarity value, without decaying, just as the second pulse is initiated.

FIGS. 18A and 18B show the effect of following this optimization scheme. In most cases, the use of a train of bipolar pulses will increase the nTMP above the single pulse maximum. For 500 ns pulses with 500 ns off times (FIG. 18A), the first pulse nTMP is approximately 0.33 V. Using a burst of pulses, this value increases to 0.44 V. The use of an optimized pulse with 4 μs on time and 500 ns off time (FIG. 18B) increases the maximum nTMP to almost 0.7 V. This optimized pulse configuration doubles the effect that the electric field has on the nuclear membrane without needing to increase the voltage applied to the system.

FIG. 19 shows the effect of nucleus size on nTMP. This has implications for the selectivity of the optimized pulse protocol. Typically, as a cell progresses (normal→benign→malignant→metastatic) the nucleus to cytoplasm ratio increases. As a result, the cell is more sensitive to the optimized bipolar pulse protocol. This can be seen by the increase in peak nTMP with increasing nucleus to cytoplasm ratio. Clinically this could translate to a zone of ablation that only affects the metastatic, infiltrative cancer cells, and spares the surrounding healthy cells. This example is emphasized in FIG. 21A-C. In another embodiment, this could enable selective nuclear transfection of metastatic cells at sublethal dosages.

According to embodiments of the invention, the nucleus-to-cytoplasm ratio can be determined by obtaining the nuclear area and the cytoplasmic area of selected types of cells and determining the ratio of the areas. One way to obtain the nuclear and cytoplasmic areas is to obtain a biopsy of a substance to be treated, such as a tissue, and measure the nuclear area and the cytoplasmic area of selected cells. The ratio of the nuclear and cytoplasmic areas can then be determined for the selected cells. Treatment protocols can be optimized based on the difference between the nucleus-to-cytoplasm ratio of cells selected as targets for the treatment and other non-target cells. For example, treatment protocols can be designed to apply electrical pulses in a manner that would treat or otherwise have an effect on certain cells but not others. The treatment parameters can be selected such as to have a desired effect (e.g., kill such cells) on target cells that have a certain nucleus-to-cytoplasm ratio or higher but have no effect (e.g., no killing) or a different effect on cells that have a nucleus-to-cytoplasm ratio lower than that of the target cells.

FIG. 20 shows the relative steady state charging behavior of the cell membrane and nuclear envelope for signals with carrier signals between 100 Hz and 1 GHz. At low frequencies, the cell membrane charges fully, mitigating the steady state maximum membrane potential of intracellular components. As the field oscillates more quickly (frequency increases), the cell membrane can no longer fully charge during a single cycle. This allows the membranes of intracellular components to charge for longer durations resulting in an increased in membrane potentials. Above approximately 500 kHz, the nuclear envelope develops a higher membrane potential than the cell membrane. As the frequency is increased above 100 MHz, the internal components cannot effectively charge during a single cycle resulting in a decreased maximum potential. This shows that there is a frequency-band over which pulses can be optimized to maximize the effect on intracellular components while minimizing effects to the cell membrane.

Analytical Modeling

FIGS. 21B-C shows the effect a bi-modal sine wave on nTMP for two cells with different nucleus to cytoplasm ratios; FIG. 21A is a key to FIGS. 21B and 21C which shows how the nuclear transmembrane potential of the two different cells is plotted. As mentioned in the methods, the applied signal consists of a superimposed low frequency (250 kHz) and high-frequency (1 MHz) electric field. The peak electric field of each individual signal is 2000 V/cm. However, when superimposed, the oscillations increase up to 4000 V/cm when the two signals are in phase. At 4000 V/cm, only the cell with the larger nucleus experiences nuclear electroporation (dotted line). An electric field of 5000 V/cm is required to achieve an equivalent level of electroporation in the cell with the smaller nucleus.

The clinical benefit of the bi-modal sine wave presented above is illustrated in FIG. 22. The two needle electrodes were spaced 0.1 cm apart and the applied voltage was set to 20 kV. The solid line (5000 V/cm electric field contour) indicates the boundary of the zone were all cells are affected by the treatment. The zone between the solid and dashed line (4000 V/cm contour) represents the region where only the infiltrate cancer cells with a larger nucleus to cytoplasm ratio would be affected. The healthy cells within this region would not be affected.

Experimental Results

FIG. 23C shows the viability of MDA-MB-231 cells exposed to bursts of 700 ns wide pulses (FIG. 23A) repeated 200 times to create an irreversible electroporation pulse train (FIG. 23B) in 0.1 S/m buffer. Viability was assessed by comparing the number of cells attached and floating in suspension to control at 1 and 16 hours post treatment. At 1000 V/cm there was minimal effect on the viability of the cells immediately and 16 hours post treatment. At 2000 V/cm and 4000 V/cm the viability reduced to 50% and 10% when considering only cells that attached to the well plates. Examination of the supinate revealed that for 4000 V/cm there was a large number of cells that failed to attach to the well plate surface, an indication that the cytoskeletal network of the cells became damaged or they were in various stages of apoptosis.

An extensive parametric study (FIGS. 24-26) was conducted on PPT8182 murine pancreatic cancer cells in media with conductivity of 0.2 S/m. Eighty bursts with total on time of 100 μs consisting of pulses with widths between 250 ns and 50 μs were delivered at field strengths of 1500 V/cm (FIG. 24), 3000 V/cm (FIG. 25), and 4000 V/cm (FIG. 26). At 1500 V/cm, pulse widths of 2 μs or greater were able to reduce the total viability to less than 50 percent after 24 hours. For pulses of 5 microseconds or greater, the viability after 24 hours was significantly reduced indicating that the cells were undergoing some form of apoptosis or delayed cell death. At 3000 V/cm pulses 1 μs or greater were reduced cell viability below 50 percent with 2 μs pulses and greater almost completely eliminating signs of cellular metabolic activity after 24 hours. At 4000 V/cm, 500 nanosecond pulses appear to induce immediate cell death (60% viability) after 1 hour and delayed cell death (30% viability) after 24 hours. Pulses greater than this induce immediate cell death (<30% viability) at one hour and further delayed cell death (<10% viability) at 24 hours. Cell viability was negligibly impacted by 250 ns pulse widths for all field strengths.

Analysis of FIGS. 24-26 show that for bursts with pulses longer than 2 μs, the viability at 1 hour and 3000 V/cm is equivalent to the viability at 24 hours and 1500 V/cm. For 1 and 2 μs pulses, the viability at 1 hour and 4000 V/cm is equivalent to the viability at 24 hours and 3000 V/cm. When applied in-vivo this will result in a zone of selective targeting enhancement in which infiltrative cancer cells will be selectively targeted. FIG. 27A shows the anticipated ablation and enhancements based on thresholds established in in-vitro experiments. The selective zone sweeps out an oval which is approximately 2 cm greater in height and width than the ablation zone, indicating that infiltrative cells within a 1 cm margin will be treated. Larger volumes, but similar enhancement zones are achieved when the field thresholds are adjusted to account for the ˜3× decrease in field thresholds observed in-vivo (FIG. 27B).

Conclusion

The present inventors showed that the frequency of the applied field and the conductivity of the suspending medium play a large role in the buildup of the TMP. In the case where electroporation is not desirable, the lowest conductivity physiologically suitable buffer should be used. Even at 0.01 S/m, the TMP will increase if continuous sine wave voltages are applied between DC and approximately 10 kHz. The extent of electroporation (both reversible and irreversible) diminishes significantly above this frequency if the field strength is held constant. This allows for significant optimization of the temporal properties of the applied electric field to maximize the effect on intracellular components.

If electroporation is desirable, as in the case of tissue ablation, it is advantageous to operate within a sufficiently conductive media. Numerical analysis of the charging times for the cell membrane indicates that 1.0 S/m is a critical conductivity. Above this, the charging time does not increase significantly, while below this, the cell may not reach its maximum TMP for short pulses. However, physiological tissue typically has conductivity between 0.1 and 0.7 S/m. The result is that short duration pulses have a mitigated effect on the cell membrane while having an enhanced effect on intracellular components. Theoretically, bursts of 4 μs pulses with 500 ns off time will result in the largest effect on the nuclear transmembrane potential and may help to further increase the lethality of the high frequency pulses.

Cells form a complex resistor-capacitor (RC) network with the fluid/media surrounding the cell. The capacitive nature of the cell membrane (C) couples with the resistance of the extracellular material (R), limiting the rate at which the cell membrane will charge to its theoretical maximum potential. In general, smaller cells have a smaller net capacitance. This in turn allows them to charge more quickly than larger cells. This charging behavior blocks the flow of current through the intracellular cytoplasm. The smallest cells in a volume of tissue will experience the smallest intracellular effects of any pulsed field. It has been shown that highly metastatic cells have a higher membrane capacitance, due to changes in the morphology of the cell membrane, even when compared to non-cancerous cell of the same size. The result of this biophysical change is that infiltrative cancerous cells will exhibit a larger net capacitance than the surrounding healthy cells. This in turn results in a longer time constant associated with the charging of the cell membranes of infiltrative cells. This lag in cell membrane charging results in an increase in charge build up on intracellular components leading to an amplified electroporation effect on the nucleus and organelles.

The result of this is that a therapeutic electric field can be applied to a volume of tissue containing healthy and cancerous cells such that only the cancerous cells in the tissue will receive the therapeutic effect. This can be selective electroporation of intracellular components for drug, gene, or protein delivery or specific triggering of an apoptotic cascade. These pulses can also be designed such that a specific volume of tissue experiences irreversible electroporation and an additional external volume will experience a targeted cancer-cell-only apoptosis inducing dose. This later scenario allows for selective targeting of infiltrative cells, such as microscopic disease, embedded in healthy tissue surrounding a tumor.

Example 2

Methods:

Numerical Modeling

A numerical model of a cell in suspension was created in COMSOL 4.2 using an impedance boundary condition scheme (G. Pucihar, T. Kotnik, B. Vali{hacek over (c)}, D. Miklav{hacek over (c)}i{hacek over (c)}, Numerical determination of transmembrane voltage induced on irregularly shaped cells, Annals of Biomedical Engineering, 34 (2006) 642-652). The solution domain consisted of a three dimensional cube with edge-lengths of 0.1 mm. At the center of this domain, two spheres were created representing the cytoplasm and nucleoplasm. Within the solution domain, the Electric Currents module was used to solve for following equations:

$\begin{matrix} {{\nabla{\cdot J}} = {Q_{j}/\left( {A/m^{3}} \right)}} & \lbrack 1\rbrack \\ {J = {\left( {\sigma + {ɛ_{0}ɛ_{r}\frac{\partial}{\partial t}}} \right){E/\left( {A/m^{2}} \right)}}} & \lbrack 2\rbrack \\ {E = {{- {\nabla U}}/\left( {V/m} \right)}} & \lbrack 3\rbrack \end{matrix}$

where U is the electric potential, E is the electric field, J is the current density, and Q is the current source. One boundary was assigned a time dependent electrical potential

U=U(t)/V  [4]

The opposing boundary was assigned as the relative ground

U=0V  [5]

The remaining boundaries were defined as electrical insulation

n·J=0/(A/m)  [6]

where n is the normal vector to the surface, J is the electrical current.

For each domain (media, cytoplasm, nucleoplasm), a separate Electric Currents physics module was used and the dependent electric potential variables U_(media), U_(cyto), U_(nuc) for the media, cytoplasm, and nucleoplasm domains were defined, respectively. These variables were then defined to calculate the voltage across the cell membrane (U_(m)) and nuclear envelope (U_(n))

U _(m) =U _(media) −U _(cyto) /V  [7]

U _(n) =U _(cyto) −U _(nuc) /V  [8]

In each Electric Currents module, the boundaries representing membranes were defined as impedance boundary conditions with reference voltages prescribed as the electric potential in the adjacent (U_(ref)) domain

$\begin{matrix} {{n \cdot \left( {J_{1} - J_{2}} \right)} = {\frac{1}{d}\left( {{\sigma \left( {U - U_{ref}} \right)} + {ɛ_{0}ɛ_{m}\frac{\partial}{\partial t}\left( {U - U_{ref}} \right)}} \right)\left( {A/m^{2}} \right)}} & \lbrack 9\rbrack \end{matrix}$

where σ is the conductivity, c is the permittivity, and d is the thickness of the cell membrane or nuclear envelope. For example, in the Media domain, the boundary representing the cell membrane was defined as an impedance boundary with reference potential of U_(cyto). In the Cytoplasm domain, the same boundary representing the cell membrane was defined as an impedance boundary with a reference potential of U_(media). The boundary was defined as a ‘thin layer’ and the electrical conductivity, relative permittivity, and surface thickness were defined using the values presented in Table 1. The nuclear envelope consists of two individual lipid membranes separated by the perinuclear space. To limit the complexity of the model and avoid improperly assessing the electrical properties of these individual components (not readily available in the literature), the inventors lumped these biological features into a single 40 nm membrane for which electrical properties representing their combined features are available.

The mesh was defined as a single free tetrahedral group with the elements between 1.8 and 10 μm on edge, resulting in 19353 tetrahedral elements. In a preliminary study of this model, finer and courser meshes were used. Simulation times more than doubled between successive refinements. The average deviation between the mesh presented here and the next successive refinement was less than 2.0% and 5.5% for the cell membrane and nuclear envelope potentials, respectively. For each parameter, solutions were found in approximately 22 minutes on a on a quad core 3.0 GHz processor with 8 GB of RAM. Results of the numerical simulations, using the values in the table in FIG. 28, were compared to those found using the analytical method presented by Kotnik and Miklavcic (T. Kotnik, D. Miklav{hacek over (c)}i{hacek over (c)}, Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields, Biophysical Journal, 90 (2006) 480-491). When calculating the maximum/minimum potentials across the cell membrane and nuclear envelope, the error between the numerical and analytical solution was 0.15%/0.15% and 1.97%/0.89%, respectively.

Cell Preparation and Experimentation

In all experiments, cells were suspended in a buffer consisting of a 5.5:1 ratio of culture media (DMEM) to low conductivity sucrose buffer (85 g sucrose, 3.0 g glucose, 7.25 mL RPMI, and 992.75 mL DI water) (L. A. Flanagan, J. Lu, L. Wang, S. A. Marchenko, N. L. Jeon, A. P. Lee, E. S. Monuki, Unique dielectric properties distinguish stem cells and their differentiated progeny, Stem Cells, 26 (2008) 656-665). The electrical conductivity of the cell suspension was measured with a conductivity meter prior to experimentation (Horiba B-173, Cole-Parmer, Vernon Hills, Ill.) to ensure a final conductivity of 0.2 S/m. Clark et al. reported that the conductivity of pancreatic tissue varied between 0.097 and 0.44 S/m for frequencies between 1 kHz and 2 MHz, respectively (D. Clark, J. Greenwell, A. Harper, A. M. Sankey, T. Scratcherd, The electrical properties of resting and secreting pancreas, The Journal of Physiology, 189 (1967) 247-260). A media conductivity of 0.2 S/m was chosen to minimize the current delivered through the sample while maintaining a conductivity value within the range of those found in in-vivo tissue. Due to limitations in the inventors' pulse generation system, higher conductivity buffers would drive the pulse delivery system outside of its safe operating region.

PPT8182 murine primary pancreatic tumor cells (J. von Burstin, S. Eser, M. C. Paul, B. Seidler, M. Brandl, M. Messer, A. von Werder, A. Schmidt, J. Mages, P. Pagel, E-cadherin regulates metastasis of pancreatic cancer in vivo and is suppressed by a SNAIL/HDAC1/HDAC2 repressor complex, Gastroenterology, 137 (2009) 361; von Burstin, 2009) were used in all experiments. These cells have been shown to replicate human pancreatic cancer in terms of histology, metastasis, and genetic alterations (von Burstin, 2009; B. Seidler, A. Schmidt, U. Mayr, H. Nakhai, R. M. Schmid, G. Schneider, D. Saur, A Cre-loxP-based mouse model for conditional somatic gene expression and knockdown in vivo by using avian retroviral vectors, Proceedings of the National Academy of Sciences, 105 (2008) 10137-10142; D. Saur, B. Seidler, G. Schneider, H. Algül, R. Beck, R. Senekowitsch-Schmidtke, M. Schwaiger, R. M. Schmid, CXCR4 expression increases liver and lung metastasis in a mouse model of pancreatic cancer, Gastroenterology, 129 (2005) 1237-1250; and M. J. PaszeK, N. Zahir, K. R. Johnson, J. N. Lakins, G. I. Rozenberg, A. Gefen, C. A. Reinhart-King, S. S. Margulies, M. Dembo, D. Boettiger, Tensional homeostasis and the malignant phenotype, Cancer cell, 8 (2005) 241-254).

Cells were cultured in DMEM (supplemented with L-glutamine, ATCC, Manassas, Va.) containing 10% fetal bovine serum (Sigma Aldrich, St. Louis, Mo.) and 1% stock solution of penicillin/streptomycin (Invitrogen, Carlsbad, Calif.) at 37° C. in 5% CO₂ in a humidified atmosphere. All cells were harvested for experiments by trypsinization at 80% confluence. Suspensions were centrifuged twice and resuspended in an experimental buffer at a concentration of 5×10⁶ cells/mL. 100 μL of cell suspension were injected into a 2 mm gap cuvette (Model 620, Harvard Apparatus, Holliston, Mass.) immediately prior to pulse delivery. A schematic of the experimental setup is shown in FIG. 29A.

The protocol for all experiments used the waveform presented in FIG. 29B. The schematic depicts an example burst which contains a repeated sequence of individual pulses. The burst begins with a positive polarity pulse followed by a 2 μs pause, then a negative polarity pulse followed by another 2 μs pause. This cycling is immediately repeated until the voltage has been delivered for a total of 100 μs (50 μs in each polarity). Eighty Bursts were delivered with a frequency of 1 Hz. Within each burst, individual pulses had a single duration of 250 ns, 500 ns, 1, 2, 5, 10, or 50 μs and therefore bursts contained 400, 200, 100, 50, 20, 10, or 2 pulses, respectively to result in equivalent energized time. The 2 μs delay time was programmed between sequential opposite polarity pulses to protect the electronics from over-voltages due to ringing. Representative examples of the bursts are shown in FIGS. 30A-30C. The cells were exposed to electric potentials with voltage-to-distance ratios (E) of 1500, 3000, and 4000 V/cm. The temperature change in the cell suspension due to pulsing was measured using fiber optic temperature probes (Luxtron FOT Lab Kit, LumaSense Technologies, Santa Clara, Calif.) inserted directly into the cell suspension.

For the in vitro studies, each of the treatment groups was repeated a minimum of three times (n=3) add experiment for each group were conducted on at least two different days. For each treatment, different experimental parameters, including sham exposure, were alternated in a random sequence. After treatment, samples were split into two equal 50 μL samples to be evaluated at 1 and 24 hour time points. The samples were kept at room temperature for approximately 20-30 minutes prior to being placed on ice (1 hour group) or moved to the incubator (24 hour group) while the remaining experimental groups were completed. Approximately one hour post exposure, viability was assessed using a trypan blue exclusion assay. Cells which had been irreversibly electroporated were unable to exclude the dye and were stained blue. Cells were counted visually using a hemocytometer and the percentage viability was determined as

$\begin{matrix} {{Viability}_{1\mspace{14mu} {hour}} = {\frac{N_{live}}{N_{total}} \cdot {100/\%}}} & \lbrack 10\rbrack \\ {r_{{viability} - {1\mspace{14mu} {hour}}} = \frac{{Viability}_{{1\mspace{14mu} {hour}} - {treatment}}}{{Viability}_{{1\mspace{14mu} {hour}} - {control}}}} & \lbrack 11\rbrack \end{matrix}$

The average viability of sham control samples in the 1 hour time group was greater than 85%. Samples to be analyzed at 24 hours were placed in separate wells in a 12-well pate containing a total of 1 mL of culture media and maintained at room temperature until the well plate was full (approximately 30 minutes). At this point the well plate was placed in an incubator at 37° C. and 5% CO₂ for 24 hours. Viability was then assessed using an Alamar blue metabolism assay (Life Technologies, Grand Island, N.Y.) using the manufactures recommended procedure. Briefly, 100 μL/mL stock Alamar blue solution was added to each well. After 4 hours, the samples were read using a spectrophotometer at 570/600 nm wavelengths. For each sample, the absorbance was measured in three separate wells and averaged. Additional measurements were taken for sample media without cells and for control cell samples which were not exposed to an electric field. The percentage viability was determined as

$\begin{matrix} {r_{{viability} - {24\mspace{14mu} {hour}}} = \frac{I_{sample} - I_{media}}{I_{control} - I_{media}}} & \lbrack 12\rbrack \end{matrix}$

where I is the relative intensity measurement from the spectrophotometer. In general, trypan blue analysis and metabolism assays complement each other quite well. They et al. previously showed that metabolism assays mirrored those from trypan blue analysis after nano-second pulsed electric field exposure (B. L. they, A. G. Pakhomov, B. W. Gregory, V. A. Khorokhorina, C. C. Roth, M. A. Rassokhin, J. A. Bernhard, G. J. Wilmink, O. N. Pakhomova, Selective cytotoxicity of intense nanosecond-duration electric pulses in mammalian cells, Biochimica Et Biophysica Acta-General Subjects, 1800 (2010) 1210-1219). The Alamar blue assay used in this study is well established for measuring cytotoxicity in mammalian cells (J. O'Brien, I. Wilson, T. Orton, F. Pognan, Investigation of the Alamar Blue (resazurin) fluorescent dye for the assessment of mammalian cell cytotoxicity, European Journal of Biochemistry, 267 (2000) 5421-5426). Reduction rates for cells seeded between 2.5×10³ and 2×10⁶ cells/mL were measured to ensure that the sham population did not completely reduce the Alamar blue solution (results not shown) and a 4 hour incubation time with 2.5×10⁵ cells/mL was determined to be optimal. Viability data for both the 1 hour and 24 hour groups were normalized to the sham control groups. Statistical analysis of the data was completed using JMP Pro V. 10.0 (SAS Institute Inc., Cary, N.C.).

Electronics

Waveforms were generated using an arbitrary function generator (AFG3021C, Tektronix Inc., Beaverton, Oreg.), which were amplified by a custom built high voltage pulse generator capable of +/−1000V outputs through high impedance loads (Applied Energetics, Tucson, Ariz., USA). Output waveforms were visualized using an oscilloscope (DPO2002B, Tektronix Inc., Beaverton, Oreg.) after the voltage was attenuated using a 50 MHz 1000× high voltage probe (P5210A, Tektronix Inc., Beaverton, Oreg.) and the current was measured using an active clamp on 50 MHz current probe (TCP305, Tektronix Inc., Beaverton, Oreg.). Short circuit protection resistors on the output limited the maximum output voltage through the 2 mm cuvettes to approximately 800 V (4000 V/cm).

Results and Discussion

Numerical Modeling

As shown in FIGS. 31A-31C, under the influence of a 1500 V/cm electric field (FIG. 31A), the potential drop across the cell membrane (U_(m)) (FIG. 31B) and nuclear envelope (U_(n)) (FIG. 31C) reaches maximums of 1.47 V and 0.28 V, respectively. U_(m) reaches 50% of the maximum value in 0.34 μs, 70.7% in 1.11 μs, and 99.99% maximum in 7.92 μs. U_(n) reaches 99.99% max in 145 ns and falls back below 70 mV in approximately 0.94 μs. This brief charging and discharging of the nuclear envelope is due to current that flows within the cytoplasm as the cell membrane is charging. This transient current increases the potential across membranes surrounding the nucleus and organelles. These intracellular components are smaller than the cell and their exposure to currents is brief resulting in a smaller potential increase.

As the positive polarity pulse falls, the cell membrane begins to discharge resulting in a second current flow within the cytoplasm in the opposite direction, as compared to the rising pulse edge. This results in the formation of a negative potential across the nuclear envelope. This negative potential reaches a minimum of −0.28 V and falls below −70 mV in a similar 0.94 μs. The rising edge of the negative polarity pulse creates a similar decrease in U_(n) creating an interesting double peak in the membrane potential of the nuclear envelope. This second peak reaches a value of −0.29 V. Though this peak is only 10 mV different than the maximum achieved by the initial pulse, it suggests that optimization of the pulse length and delay time between pulses could result in an increased effect on intracellular membranes.

In this Example, the inventors elected to disregard the effects of electroporation on the cell membrane to simplify their analysis. However, in the case of electroporation, current would be allowed to flow through the cytoplasm and a sustained potential would be induced across the intracellular membranes.

Analysis of Experimental Parameters

FIGS. 32A-C presents a parametric analysis of variables which can be controlled experimentally. The pulse duration, shown in FIG. 32A, directly impacts the maximum U_(m) achieved and the duration that U_(m) is elevated above the 1V critical threshold. Pulses that are shorter than 1 μs do not elevate the U_(m) above this threshold. As pulse duration increases beyond 1 μs, U_(m) saturates to a maximum value of 1.47 V. In contrast, because U_(n) rises rapidly in comparison to the U_(m), the effects on the nuclear envelope are minimally impacted by the pulse duration. Regardless of pulse width, the U_(n) reaches a maximum value within 145 ns. For pulses 1 μs or less, the U_(n) does not completely return to zero before the falling edge of the positive pulse, muting the negative U_(n) response.

It has been observed that pore formation behavior occurs within 1 μs after U_(m) is elevated above 1V, quenching further increases in potential (K. Kinosita, I. Ashikawa, N. Saita, H. Yoshimura, H. Itoh, K. Nagayama, A. Ikegami, Electroporation of cell membrane visualized under a pulsed-laser fluorescence microscope, Biophysical Journal, 53 (1988) 1015-1019), after which new pore formation is limited and pore expansion takes over as the dominant phenomena (K. Kinosita, T. Y. Tsong, Formation and resealing of pores of controlled sizes in human erythrocyte membrane, (1977); K. Kinosita, T. Y. Tsong, Voltage-induced pore formation and hemolysis of human erythrocytes, Biochimica et Biophysica Acta (BBA)-Biomembranes, 471 (1977) 227-242). At the field strengths presented here, pulses 1 μs in duration and shorter may not efficiently result in pore expansion within the cell membrane (O. M. Nesin, O. N. Pakhomova, S. Xiao, A. G. Pakhomov, Manipulation of cell volume and membrane pore comparison following single cell permeabilization with 60- and 600-ns electric pulses, Biochimica et Biophysica Acta (BBA)-Biomembranes, 1808 (2011) 792-801).

The conductivity of the sample media, FIG. 32B, contributes significantly to the charge-discharge behavior of the cell membrane and the nuclear envelope. At low media conductivities (0.01 S/m), the media presents a significant resistance to current flow and the cell membrane charges slowly. This low conductivity media minimizes the current which can flow through the cytoplasm, muting the maximum U_(n) achieved. As the media conductivity increases, the cell membrane charges more quickly, saturating as the conductivity is increased above 1 S/m. Based on these simulations, a media conductivity of 0.2 S/m experimentally is a compromise between membrane charging times and current output required from the pulse generator. Increasing media conductivity may have resulted in slightly faster membrane charging times.

The delay between positive and negative polarity pulses, FIG. 32C, has a negligible effect on the transmembrane potential (U_(m)); though, it has a significant impact on the nuclear envelope (U_(n)). The falling edge of the positive pulse results in a negative potential build up on the nuclear envelope. U_(n) reaches a relative maximum approximately 100 ns after the falling edge of each pulse. For long delays between pulses, this potential decays back to zero. In contrast, as the delay is contracted, U_(n) is compounded by the rising edge of the negative polarity pulse. Ultimately, as the delay is decreased to 0.1 μs, an effective doubling of the U_(n) is achieved. Based on these simulations, bursts with a 100 ns delay between changes in pulse polarity will achieve the greatest potential across the nuclear envelope. Counterintuitively, including zero inter-pulse delay results in a lower U_(n) than the 100 ns case (results not shown). To achieve a doubling in U_(n), the potential across the nuclear envelope must be allowed to decay back to zero before the applied voltage is turned off. In this scenario, all pulses which are 0.94 μs in duration or longer resulted in approximately a 2× increase in U_(n) versus the single pulse maximum.

The role of DNA damage in the PEF apoptotic cascade is not fully understood and the nucleus is not typically the target for PEF therapy. However, intrinsic and extrinsic apoptotic cell death processes are associated with field strength dependent effects on mitochondria and the endoplasmic reticulum. If waveform optimization can be used to double the increase in the transmembrane potential of these organelles, as shown in FIG. 32C, then a lower amplitude electric field would be needed to induce the associated apoptotic cascades. Alternatively, by finely tuning the pulse widths and inter-pulse delays it may be possible to enhance DNA damage processes allowing for further study of this mechanism in the PEF apoptotic cascade. Unfortunately, experimental investigation of well controlled 100-500 ns inter-pulse delay scenarios was inhibited by ringing in the output voltages of the inventors' current system and are left as the subject of future work.

Analysis of Cell Electrical Properties

Electrical properties for the cell membrane, nuclear envelope, cytoplasm, and nucleoplasm are readily available in the literature (B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J. D. Watson, Molecular Biology of the Cell, 3rd edition, Garland Science, New York, 1994; P. R. Gascoyne, R. Pethig, J. P. Burt, F. F. Becker, Membrane changes accompanying the induced differentiation of Friend murine erythroleukemia cells studied by dielectrophoresis, Biochimica et Biophysica Acta (BBA)-Biomembranes, 1149 (1993) 119-126; J. Yang, Y. Huang, X. J. Wang, X. B. Wang, F. F. Becker, P. R. C. Gascoyne, Dielectric properties of human leukocyte subpopulations determined by electrorotation as a cell separation criterion, Biophysical Journal, 76 (1999) 3307-3314; I. Ermolina, Y. Polevaya, Y. Feldman, B.-Z. Ginzburg, M. Schlesinger, Study of normal and malignant white blood cells by time domain dielectric spectroscopy, Dielectrics and Electrical Insulation, IEEE Transactions on, 8 (2001) 253-261; J. Gimsa, T. Müller, T. Schnelle, G. Fuhr, Dielectric spectroscopy of single human erythrocytes at physiological ionic strength: dispersion of the cytoplasm, Biophysical Journal, 71 (1996) 495-506; and K. Asami, Y. Takahashi, S. Takashima, Dielectric properties of mouse lymphocytes and erythrocytes, Biochimica et Biophysica Acta (BBA)-Molecular Cell Research, 1010 (1989) 49-55). Subuncu et al. report that a cytoplasmic conductivity of between 0.3 and 0.6 S/m (A. C. Sabuncu, J. A. Liu, S. J. Beebe, A. Beskok, Dielectrophoretic separation of mouse melanoma clones, Biomicrofluidics, 4 (2010) 021101). Labeed et al. report increases in conductivity from 0.28 S/m to 0.45 S/m as cells begin to undergo apoptosis (F. H. Labeed, H. M. Coley, M. P. Hughes, Differences in the biophysical properties of membrane and cytoplasm of apoptotic cells revealed using dielectrophoresis, Biochimica et Biophysica Acta (BBA)-General Subjects, 1760 (2006) 922-929). Ron et al. report a conductivity of 0.724 S/m and 0.93 S/m for pre-osteoblast cells and normal canine kidney cells, respectively (A. Ron, R. R. Singh, N. Fishelson, I. Shur, R. Socher, D. Benayahu, Y. Shacham-Diamand, Cell-based screening for membranal and cytoplasmatic markers using dielectric spectroscopy, Biophysical chemistry, 135 (2008)) 59-68. Mulhall el al. found cytoplasm conductivities of 0.71, 0.42, 0.26, and 0.25 S/m for normal keratinocytes, abnormal keratinocytes, for two different malignant keratinocytes, respectively (H. Mulhall, F. Labeed, B. Kazmi, D. Costea, M. Hughes, M. Lewis, Cancer, pre-cancer and normal oral cells distinguished by dielectrophoresis, Analytical and Bioanalytical Chemistry, 401 (2011) 2455-2463). Additionally, Chen et al. show that drug resistant cells have a lower cytoplasmic conductivity than non-drug resistant cells (J. Chen, Y. Zheng, Q. Tan, E. Shojaei-Baghini, Y. L. Zhang, J. Li, P. Prasad, L. You, X. Y. Wu, Y. Sun, Classification of cell types using a microfluidic device for mechanical and electrical measurement on single cells, Lab on a Chip, 11 (2011) 3174-3181). These results provide evidence of decreasing cytoplasmic conductivity as cells transition from benign to malignant.

Yuan et al. show an increase in nucleus-to-cytoplasm (NCR) ratio from 0.45 to 0.49 and from 0.40 to 0.49 as cancer cells achieve drug resistance. Similarly, Helczynska et al. show histologically, that the NCR increases from 0.3 to 0.8 as a function of tumor grade, with higher NCRs for increasingly malignant cancers (K. Helczynska, Å. Kronblad, A. Jögi, E. Nilsson, S. Beckman, G. Landberg, S. Påhlman, Hypoxia promotes a dedifferentiated phenotype in ductal breast carcinoma in situ, Cancer Research, 63 (2003) 1441-1444). Salmanzadeh et al. showed that the specific membrane capacitance of a syngeneic cell line increased from 15.39 mF/m² to 26.42 mF/m² as the cells became successively more malignant (A. Salmanzadeh, M. B. Sano, R. C. Gallo-Villanueva, P. C. Roberts, E. M. Schmelz, R. V. Davalos, Investigating dielectric properties of different stages of syngeneic murine ovarian cancer cells, Biomicrofluidics, 7 (2013) 011809). This translates into an increase in relative membrane permittivity from 8.70 to 14.92.

A parametric analysis was conducted using cytoplasmic conductivity values of 0.7, 0.475, and 0.25 S/m, an NCR of 0.3, 0.55, and 0.8, and a membrane permittivity of 9, 12, and 15 to represent this transition from benign to intermediate to metastatic, respectively. The present inventors modeled the response of a ‘benign’ cell having cytoplasmic conductivity of 0.7 S/m, NCR of 0.3, and membrane permittivity of 8.7. A ‘metastatic’ cell was modeled as having cytoplasmic conductivity of 0.25 S/m, NCR of 0.8, and a membrane permittivity of 15. All other values (Table 1) were held constant.

The nucleus-to-cytoplasm ratio (NCR), FIG. 33A, has a negligible effect on U_(m) and a measurable effect on U_(n). As expected from electromagnetic theory (P. Marszalek, D. Liu, T. Y. Tsong, Schwan equation and transmembrane potential induced by alternating electric field, Biophysical Journal, 58 (1990) 1053-1058), the potential across an the nuclear envelope is related to the equation

ΔU=1.5rE cos θ/V  [13]

where r is the radius of the nucleus and E is the electric field which the cell is exposed to. However, other dielectric properties of the nucleus may affect the membrane charging time (T. Kotnik, D. Miklav{hacek over (c)}i{hacek over (c)}, Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields, Biophysical Journal, 90 (2006) 480-491; K. H. Schoenbach, S. J. Beebe, E. S. Buescher, Intracellular effect of ultrashort electrical pulses, Bioelectromagnetics, 22 (2001) 440-448). As the NCR increases in FIG. 33A, U_(n) also increases. The cytoplasm conductivity, FIG. 33B, has a negligible impact on the maximum amplitude of U_(m) and U_(n), however lower conductivity values result in a slightly higher U_(n) values. The permittivity of the cell membrane, FIG. 33C, impacts the charge and discharge of the cell membrane and the nuclear envelope. A higher permittivity causes the U_(m) to increase slightly slower than the lower permittivity cells. This slower charging time of the cell membrane results in the nuclear envelope reaching a slightly higher transmembrane potential.

Numerical Simulation of Experimental Pulses

The simulation results of FIGS. 31A-33C represent the idealized response to a perfect square wave with 10 ns rise and fall times. The waveforms exhibited ringing effects on the rising edge and after the falling edge as shown in FIGS. 34A and 34C. FIGS. 34B and 34D shows the transmembrane potential (U_(m)) and trans-nuclear membrane potential (U_(n)) resulting from experimental 250 ns and 1 μs pulses, respectively. As in the idealized case, the falling edge of the pulses results in an increased U_(n) in the opposite polarity. The ringing in the output waveform causes an additional minor increase in U_(n). At 1500 V/cm the first rising edge of a 250 ns pulse results in an U_(n) amplitude maximum of 0.21 V. The falling edge and ringing of the same pulse results in a maximum U_(n) amplitude of 0.25 V, a 19% increase.

For a 1 μs experimental pulse, |U_(m)| reaches a maximum of 1.24 V while |U_(n)| reaches a maximum of 0.32 V. The magnitude of U_(m) for this experimental pulse is approximately equal to the ideal value predicted in FIG. 32A (1.21V). However, the magnitude of U_(n) for this experimental pulse (0.32 V) is greater than the value predicted in FIG. 32A (0.29 V). This is due to the ringing which occurs after the experimental pulses fall back to zero.

As the pulse length increases, the initial U_(n) response is allowed to fall back towards zero. The result is that for longer pulses, the negative going edge and subsequent ringing have an increased effect. For similar field strengths, a 5 μs pulse results in U_(n) amplitude change from 0.24 V to 0.36 V, a 50% increase (not shown). For these cases, the peak amplitude of the ringing is 46-52% that of the pulse amplitude and lasts for less than 200 ns.

Experimental Results

Experiments were conducted with an initial sample temperature between 22 and 25° C. At 4000 V/cm all experimental groups resulted in a temperature rise less than 3.5° C. Representative temperature profiles for experiments with 50 μs and 250 ns constitutive pulses are shown in FIG. 35. The temperature increase for bursts with 250 ns pulses is similar to the increase for longer duration pulses. This is likely due to the delivery of an equivalent quantity of energy in each burst regardless of the duration of the constituent pulses. The starting temperature of the experiments ensured that the temperature never rose above 37° C., mitigating the possibility of temperature as a confounding factor, affecting the viability of cells.

FIGS. 36A-36C show the viability of the samples 1 and 24 hours after treatment for field strengths of (FIG. 36A) 1500 V/cm, (FIG. 36B) 3000 V/cm, and (FIG. 36C) 4000 V/cm. There is a clear inverse relationship between constituent pulse length and viability, with longer duration pulses resulting in a lower viability for both the 1 and 24 hour viability studies.

Specifically, at 1500 V/cm, bursts containing 50 μs pulse (2×) resulted in a 1 hour post-treatment viability of 31% which reduced to 3% after 24 hours. The 1500 V/cm bursts containing pulses between 250 ns (400×) and 10 μs (10×) resulted in 1 hour viabilities above 50% and notably, pulses 2 μs (5×) and shorter had viabilities of 85% or greater, similar to sham treatments. In between the 1 and 24 hour time-points, the viability fell by an average of 20% for cells exposed to 1500 V/cm over all constituent pulses. For this field strength, bursts containing 10 μs pulses had the largest change in viability over 24 hours, 49%, while 250 and 500 ns pulses resulted in a negligible change in viability compared to controls. Significant changes in viability occurred between the 1 and 24 hour time points for bursts with pulses 2 μs and longer. It is interesting that 10 and 50 μs pulses resulted in delayed cell death, however, the mechanism of action is unclear.

Cell viability was significantly lower for 3000 V/cm versus 1500 V/cm bursts when the pulse duration was 1 μs or longer. After 24 hours, the viability for 2 to 50 μs pulses reduced to less than 5% at 3000 V/cm. Between 3000 V/cm and 4000 V/cm, the most significant impact on viability occurred for 500 ns pulses. For all field strengths, 250 ns pulses have a minimal impact on cell viability.

For bursts containing 250 ns pulses, the difference in viability after 1500, 3000, and 4000 V/cm treatments was not statistically significant (α≦0.1). All other pulse-widths had a statistically significant difference between the 1500 V/cm and 3000 V/cm treatments at each timepoint (α≦0.06). Between the 3000 and 4000 V/cm treatments, 5 μs (1 hour), 500 ns (1 hour), and 500 ns (24 hour) groups had statistically different viabilities (α≦0.03)

Interestingly, this study shows that viability is not directly correlated to the energy dose delivered. This conforms to the results presented by others that electropermeabilization (A. Ma{hacek over (c)}ek-Lebar, D. Miklav{hacek over (c)}i{hacek over (c)}, Cell electropermeabilization to small molecules in vitro: control by pulse parameters, Radiology and Oncology, 35 (2001)) and lethal (B. L. Ibey, A. G. Pakhomov, B. W. Gregory, V. A. Khorokhorina, C. C. Roth, M. A. Rassokhin, J. A. Bernhard, G. J. Wilmink, O. N. Pakhomova, Selective cytotoxicity of intense nanosecond-duration electric pulses in mammalian cells, Biochimica Et Biophysica Acta-General Subjects, 1800 (2010) 1210-1219) effects of mono-polar pulses of different pulse widths exhibit a complex relationship that cannot be correlated to the quantity of energy delivered alone. The inverse correlation between pulse length and toxicity presented may be related to the cell membrane charging time, calculated here as between 1.11 and 7.92 μs. FIGS. 37A-L shows the effect of multiple pulses within each burst on the time in which U_(m) and U_(n) are elevated above critical thresholds. A single cycle of 1500 V/cm 250 ns pulses, one positive and one negative, increases U_(m) above 1 V for only 200 ns total. However, the cumulative effect of 200 cycles per burst (400 total pulses) increases U_(m) above 1 V for approximately 40 μs. At 1500 V/cm (FIG. 9A-B) time above the 1 V threshold increases as constitutive pulse width (Δt_(p)) is increases. This process reaches a maximum of approximately 99.8 μs for bursts with 50 μs constitutive pulse widths, which only have one cycle. At 3000 and 4000 V/cm, FIGS. 37E-F, I-J, bursts of shorter pulses elevate U_(m) above 1 V for a longer duration than those with longer pulse durations, however, this appears to have a negligible impact on cell viability. Though not examined here, pulses energized for less than the membrane charging time may result in limited pore expansion, minimizing lethal effects.

At 1500 V/cm, none of the pulse durations elevated U_(n) above thresholds of 0.5, 0.75, or 0.9 V (FIGS. 37C-D). 0.7 and 0.9 V are shown a surrogates for the 1.0 V threshold which was not reached for any simulation at the highest voltage (4000 V) and 0.5 V is used to approximate the onset of reversible electroporation (A. M. Lebar, G. C. Troiano, L. Tung, D. Miklavcic, Inter-pulse interval between rectangular voltage pulses affects electroporation threshold of artificial lipid bilayers, NanoBioscience, IEEE Transactions on, 1 (2002) 116-120; A. Polak, D. Bonhenry, F. Dehez, P. Kramar, D. Miklav{hacek over (c)}i{hacek over (c)}, M. Tarek, On the Electroporation Thresholds of Lipid Bilayers: Molecular Dynamics Simulation Investigations, The Journal of membrane biology, 246 (2013) 843-850). At 3000 V/cm (FIGS. 37G-H), all pulse durations are able to increase U_(n) above the 0.5 V threshold. The cumulative impact of a full burst results in U_(n) increasing above the 0.5 V threshold for a substantially longer duration for shorter constitutive pulses. At 4000 V/cm (FIGS. 37K-L), some pulse durations are able to elevate U_(n) above the 0.75 and 0.9 V thresholds. Interestingly, 500 ns pulses result in greater cumulative time above all of the thresholds than any other pulse durations. This may help explain why 500 ns bursts resulted in significant changes in viability between 1 and 24 hours and 250 ns did not.

For all bursts containing pulses 1 μs in duration or longer, the viability at 3000 V/cm after 24 hours is lower than the corresponding viability at 4000 V/cm after one hour. This has interesting implications for in-vivo applications as it indicates that ablation sizes may grow over time and that immediate observation may be inadequate to predict the total volume treated. From the numerical simulations, it is anticipated that cells with a larger cytoplasm-nucleus ratio will achieve higher U_(n) amplitudes than cells of similar size with a smaller ratio. A high nucleus-cytoplasmic ratio (NCR) has been associated with the aggressiveness of malignant cells and is used as a parameter in grading cancers (K. Seibert, S. M. Shafie, T. J. Triche, J. J. Whang-Peng, S. J. O'Brien, J. H. Toney, K. K. Huff, M. E. Lippman, Clonal variation of MCF-7 breast cancer cells in vitro and in athymic nude mice, Cancer research, 43 (1983) 2223-2239; Y. Shimizu, S. Kamoi, S. Amada, F. Akiyama, S. G. Silverberg, Toward the development of a universal grading system for ovarian epithelial carcinoma, Cancer, 82 (1998) 893-901; A. Malpica, M. T. Deavers, K. Lu, D. C. Bodurka, E. N. Atkinson, D. M. Gershenson, E. G. Silva, Grading ovarian serous carcinoma using a two-tier system, The American journal of surgical pathology, 28 (2004) 496-504; and S. G. Silverberg, Histopathologic grading of ovarian carcinoma: A review and proposal, Inter. J. of Gynecological Pathology, 19 (2000) 7-15).

Additionally, it has been shown that an increase in invasiveness and metastatic potential has been correlated to cell membrane ruffling, which leads to higher membrane capacitances in aggressive cells (A. Salmanzadeh, M. B. Sano, R. C. Gallo-Villanueva, P. C. Roberts, E. M. Schmelz, R. V. Davalos, Investigating dielectric properties of different stages of syngeneic murine ovarian cancer cells, Biomicrofluidics, 7 (2013) 011809; A. Salmanzadeh, H. Kittur, M. B. Sano, P. C. Roberts, E. M. Schmelz, R. V. Davalos, Dielectrophoretic differentiation of mouse ovarian surface epithelial cells, macrophages, and fibroblasts using contactless dielectrophoresis, Biomicrofluidics, 6 (2012) 024104; and A. Salmanzadeh, E. S. Elvington, P. C. Roberts, E. M. Schmelz, R. V. Davalos, Sphingolipid Metabolites Modulate Dielectric Characteristics of Cells in a Mouse Ovarian Cancer Progression Model, Integr. Biol., (2013)). In numerical simulations (FIG. 33D), a normal cell model experiences a |U_(n)|≈0.14V while a cancer cell model reaches |U_(n)|≈0.32V. The nucleus in the cancer cell model reaches a potential approximately 2 time higher than the normal cell model as a result of changes in NCR. This effect is amplified further if the delay between pulses is reduced to 100 ns (FIG. 33E) where |U_(n)|≈0.6 V for the cancer cell model. It is anticipated that malignant cells will experience an increased response to bi-polar pulses due the increase in lipid-bilayer charging time, resulting from an increased membrane capacitance, coupled with increased nucleus-cytoplasm ratio. However, future work will be required to determine if these burst have an increased efficiency at targeting aggressive cells.

Conclusions

The present inventors found, through finite element simulations, that the charge-discharge behavior of the cell membrane impacts the electric field experienced by intracellular components. This simplified model has some limitations. Cells were modeled as simple spheres to reflect the shape of the cells in their non-adhered state. In vivo, cells typically take on more complex, elongated, or spindled shapes which can alter the effects of pulsed electric fields on transmembrane potential. Additionally, cells in tissue are affected by local inhomogeneity and the responses of cells in their immediate vicinity which was not accounted for here.

Cytoplasm-nucleus ratio, cytoplasm conductivity, and cell membrane permittivity play a significant role in the charging characteristics of the nuclear envelope. Experimentally the inventors found that bursts of bi-polar square waves increased the media temperature less than 3.5° C. when the total energized time per burst was held constant at 100 μs and eighty bursts were delivered. The resulting cellular responses are therefore limited to those related directly to non-thermal phenomena. For the bursts of bi-polar pulses presented, there exists an inverse correlation between pulse-width and toxicity despite the delivery of equal quantities of energy. The changes in cellular viability over 24 hours post treatment show presence of both instantaneous and delayed cell death processes, however, the exact mechanisms are unknown.

To the best of the inventors' knowledge, this is the first experimental parametric analysis on the effects of bi-polar square wave bursts with pulses between 0.25 and 50 μs. In the 3000 V/cm treatment groups, cell viability was reduced to 4.0%, 0.5%, 0.3%, and 1.0% for bursts containing 2, 5, 10, and 50 μs pulses, respectively. In the 4000 V/cm treatment groups, cell viability was reduced to 3.8%, 1.4%, 0.9%, 0.8%, and 0.8% for bursts containing 1, 2, 5, 10 and 50 μs pulses, respectively. Rubinsky et al. (J. Rubinsky, G. Onik, P. Mikus, B. Rubinsky, Optimal Parameters for the Destruction of Prostate Cancer Using Irreversible Electroporation, The Journal of Urology, 180 (2008) 2668-2674) showed that ten 100 μs monopolar pulses at 2000 V/cm resulted in a viability of 70%. In the same study, they showed that seventy-five 100 μs monopolar pulses at 250 V/cm resulted in a viability of 10-20% while ninety 100 μs monopolar pulses at 250 V/cm reduced viability to 0-10%. Arena et al. (C. B. Arena, C. S. Szot, P. A. Garcia, M. N. Rylander, R. V. Davalos, A Three-Dimensional In vitro Tumor Platform for Modeling Therapeutic Irreversible Electroporation, Biophysical Journal, 103 (2012) 2033-2042 (“Arena et al., 2012”)) showed that after eighty 100 μs monipolar pulses at 1500 V/cm, cell viability was approximately 8% and this protocols is consistent with those currently being employed successfully in clinical applications of irreversible electroporation in the prostate (G. Onik, B. Rubinsky, Irreversible Electroporation: First Patient Experience Focal Therapy of Prostate Cancer, in: B. Rubinsky (Ed.) Irreversible Electroporation, Springer Berlin Heidelberg, 2010, pp. 235-247), pancreas (R. C. Martin II, K. McFarland, S. Ellis, V. Velanovich, Irreversible electroporation therapy in the management of locally advanced pancreatic adenocarcinoma, Journal of the American College of Surgeons, 215 (2012) 361-369), and liver (R. Cannon, S. Ellis, D. Hayes, G. Narayanan, R. C. Martin, Safety and early efficacy of irreversible electroporation for hepatic tumors in proximity to vital structures, Journal of Surgical Oncology, (2012)). The comparable level of toxicity resulting from the bi-polar burst protocol presented here indicates that it may be advantageous in in-vivo therapies where muscle contractions due to longer duration mono-polar pulses are undesirable.

Example 3

Materials and Methods

Collagen Hydrogel Tumor Mimics

PPT8182 murine primary pancreatic tumor cells (von Burstin, 2009), shown to replicate human pancreatic cancer in terms of histology, metastasis, and genetic alterations (von Burstin, 2009; Seidler, B., et al. A Cre-loxP-based mouse model for conditional somatic gene expression and knockdown in vivo by using avian retroviral vectors. Proceedings of the National Academy of Sciences 105, 10137-10142 (2008); Saur, D., et al. CXCR4 expression increases liver and lung metastasis in a mouse model of pancreatic cancer. Gastroenterology 129, 1237-1250 (2005); PaszeK, M. J., et al. Tensional homeostasis and the malignant phenotype. Cancer cell 8, 241-254 (2005); and Szot, C. S., Buchanan, C. F., Freeman, J. W. & Rylander, M. N. 3D in vitro bioengineered tumors based on collagen I hydrogels. Biomaterials 32, 7905-7912 (2011)) were used in the 3D tumor platform experiments. Cells were cultured in Dulbecco's Modified Eagle Medium (DMEM) supplemented with L-glutamine (ATCC, Manassas, Va.) containing 10% fetal bovine serum (FBS; Sigma Aldrich, St. Louis, Mo.) and 1% penicillin/streptomycin (Invitrogen, Carlsbad, Calif.) at 37° C. in 5% CO₂ in a humidified atmosphere. All cells were harvested for experiments by trypsinization at 80% confluence.

FIGS. 38A-B show that high-frequency BEAM treatment replaces the single monopolar pulse (FIG. 38A) with a burst of higher frequency bi-polar pules (FIG. 38B). Collagen I hydrogels, shown in FIG. 38C, were produced as described previously (Szot, C. S., Buchanan, C. F., Freeman, J. W. & Rylander, M. N. 3D in vitro bioengineered tumors based on collagen I hydrogels. Biomaterials 32, 7905-7912 (2011)). Briefly, Sprague Dawley rat tail tendons were excised and allowed to dissolve under agitation overnight in 10 mM HCl at room temperature. The resulting monomeric collagen suspension was centrifuged at 22,500×g for 30 min, and the supernatant was decanted and stored at 4° C. until later use. The collagen hydrogels were formed by neutralizing the collagen I in HCl with a buffer containing 10× concentrated DMEM (supplemented with 4.5 g/L glucose, L-glutamine, sodium pyruvate, and sodium bicarbonate; Mediatech Inc., Manassas, Va.), 1N NaOH, and deionized H₂O to obtain a final concentration of 8 mg/mL at a pH of 7.4. The PPT8182 cells were suspended in the neutralizing buffer at a final seeding density of 1×10⁶ cells/mL and then mixed with the collagen I solution. The collagen-cell suspension was pipetted into 10 mm diameter cylindrical molds to achieve a thickness of 3 mm after polymerization. Following a 20 min gelation period at 37° C., the hydrogels were removed from the molds and cultured in complete media for 18 hours prior to pulse delivery.

Electronics and Protocols

A custom pulse generation system was used to deliver bursts of bi-polar pulses with constitutive pulse widths of 250 ns, 500 ns, 1 μs, 2 μs, 5 μs, 10 μs, and 50 μs. A 500Ω resistor was placed in parallel with the load to ensure proper pulse shaping and to protect against delivering pulses to an open circuit. Custom electrodes were made from hollow 1.27 mm diameter dispensing needles (Howard Electronic Instruments Inc., El Dorado, Kans.) with a 2.0 mm edge-to-edge separation distance.

A pilot study was conducted at 540 V_(peak) and a total energized time of 100 μs for all pulse widths. This protocol used 400, 200, 100, 50, 20, 5, or 2 pulses to comprise a burst, with individual pulse durations of 250 ns, 500 ns, 1 μs, 2 μs, 5 μs, 10 μs, or 50 μs, respectively. The ablation zones at 540 V_(peak) for bursts containing pulses 1 μs or less were not well formed ovals surrounding the electrodes. Instead, dead cells occupied small triangular zones which extended, but did not connect between the two electrodes. The electric field intensity changed rapidly in this zone resulting in large variations in the calculation of electric field thresholds. To avoid this, a higher voltage of 650 V was used for the 250 ns, 500 ns, 1 μs and 2 μs groups. To facilitate comparison between groups, a simplified electrical dose formula was used.

Dose=V ² *T _(p) *n*N[V ² s]  [14]

where V is the applied voltage, T_(p) is the pulse width, n is the number of pulses per burst, and N is the number of bursts per treatment which was held a constant 80. The 540 V_(peak) group had an approximate dose of 2300 V²s. At 650 V_(peak), 256, 128, 64, and 32 pulses were used for the 250 ns, 500 ns, 1 μs, and 2 μs groups, respectively. This resulted in an approximate dose of 2200 V²s. An additional 2 μs group at 250 V_(peak) with 216 pulses an approximate dose of 2000 V²s was also conducted to compare effects of energy and lethal electric field threshold.

To explore the effect of burst energized time, a set of experiments were conducted with 80 bursts containing 2 μs pulses at 540V. Pulses were repeated 2, 24, or 50 times per burst with a 2 μs inter-pulse delay. To compare ‘diffuse’ and ‘burst’ delivery of pulses an additional group of 50 pulses per second was tested. In this group, one positive and one negative pulse were delivered, with a 2 μs inter-pulse delay, every 20 ms for a total of 80 seconds. This is the only group presented in which a 1 second inter-burst delay was not used.

To explore the effect of treatment time, a set of experiments were conducted with eight bursts. These groups had 2 μs, 50 μs, and 100 μs pulses which were repeated 50, 2, and 1 times per burst, respectively. The experimental parameters are summarized in the table in FIG. 39. All parameters were repeated a minimum of three (n=3) times.

Sample Processing

At 24 hours after treatment, normal culture media was replaced with 2.5 mL of media supplemented with 4 μM Calcein AM (live stain, λ_(em)=515 nm, Invitrogen, Eugene, Oreg.) and incubated at 37 C for 30 minutes. Five minutes prior to visualization, the media was supplemented with 75 μL of 1.5 mM propidium iodide (PI; dead stain, λ_(em)=617 nm, Invitrogen, Eugene, Oreg.) for 5 minutes. Finally, the hydrogels were rinsed with PBS to flush out any unabsorbed dyes and increase the signal to noise ratio. A Leica DMI 6000 fluorescent microscope with a 20× objective (Leica Microsystems Inc., Buffalo Grove, Ill.) was used to tile a set of images and reconstruct an entire plane of the treated scaffolds just under the surface.

Analysis of Electric Field Thresholds in Tissue Mimics

Finite element models were created in COMSOL Multiphysics (Version 4.2a, COMSOL Inc., Burlington, Mass.). The collagen hydrogels were modeled as a 3 mm thick cylinder with a 5 mm radius and conductivity of 1.2 S/m. Cylinders representing the 1.27 mm outer diameter electrodes were offset such that their edge-to-edge distance was equal to 2 mm. Within the solution domain, the Electric Currents module was used to solve for the following equations:

$\begin{matrix} {{\nabla{\cdot J}} = {Q_{j}/\left( {A/m^{3}} \right)}} & \lbrack 1\rbrack \\ {J = {\left( {\sigma + {ɛ_{0}ɛ_{r}\frac{\partial}{\partial t}}} \right){E/\left( {A/m^{2}} \right)}}} & \lbrack 2\rbrack \\ {E = {{- {\nabla U}}/\left( {V/m} \right)}} & \lbrack 3\rbrack \end{matrix}$

where U is the electric potential, E is the electric field, J is the current density, Q is the current source, a is the conductivity, ∈_(r) is the relative permittivity, and ∈₀ is the permittivity of free space. The boundaries surrounding one electrode were assigned a constant electrical potential

U=U[V]  [15]

The boundaries of the other electrode were assigned as a relative ground

U=0/V  [5]

The remaining boundaries were defined as electrical insulation

n·J=0/(A/m)  [6]

where n is the normal vector to the surface, J is the electrical current.

Changes in temperature due to Joule heating were calculated for 540 V and 100 energized time over 80 seconds using a modified duty cycle approach (Arena, C. B., et al. High-Frequency Irreversible Electroporation (H-FIRE) for Non-thermal Ablation without Muscle Contraction. Biomed Eng Online 10(2011); Neal, R. E., 2nd, Garcia, P. A., Robertson, J. L. & Davalos, R. V. Experimental Characterization and Numerical Modeling of Tissue Electrical Conductivity during Pulsed Electric Fields for Irreversible Electroporation Treatment Planning. IEEE Trans Biomed Eng 59, 1076-1085 (2012)). The temperature distribution (T) was obtained by transiently solving a modified heat conduction equation:

$\begin{matrix} {{\rho \; c\frac{\partial T}{\partial t}} = {{\nabla{\cdot \left( {k{\nabla T}} \right)}} + {\frac{\tau \left( {\sigma {E}^{2}} \right)}{P}\left\lbrack \frac{J}{m^{3} \cdot s} \right\rbrack}}} & \lbrack 16\rbrack \end{matrix}$

where τ is the pulse duration, P is the period of the pulses, k is the thermal conductivity, c is the specific heat at constant pressure, and p is the density. Outer boundaries were treated as convective cooling

$\begin{matrix} {{{- n} \cdot \left( {{- k}{\nabla T}} \right)} = {{h\left( {T_{ext} - T} \right)}\left\lbrack \frac{W}{m} \right\rbrack}} & \lbrack 17\rbrack \end{matrix}$

with an exterior temperature (T_(ext)) of 22° C. and a heat transfer coefficient (h) of 25 (W m⁻² K⁻¹). Intermediate time stepping was used to ensure that at least one time step was taken each second. Simulations at 540 V showed that thermal effects resulted in a negligible impact on the electric field distribution and changes in conductivity due to temperature increases were neglected in subsequent models to minimize computational time. Changes in conductivity due to electroporation were similarly neglected due to the low concentration of cells within the scaffold. To replicate the values measured experimentally, the voltage on one electrode was swept between 470-700V, in steps of 10V, and the other was held at ground.

Tiled images near the surface of the hydrogels (representative examples in FIGS. 38D-G) were examined using ImageJ (version 1.43u, National Institutes of Health, USA). The width and height of the region of cells that had taken up PI (dead region) was measured. These values were then correlated to the electric field intensity from the numerical simulations to determine the electric field threshold required for cell death (Arena et al., 2012). Statistical analysis of the data was completed using JMP (Version 10.0 Pro, SAS Institute Inc., Cary, N.C.) with a confidence level of 99% (α=0.01).

Murine Tumor Model

This study was approved by the Virginia Tech Institutional Animal Care and Use Committee. 6-7 week old Hsd:Athymic Nude-Foxn1^(nu) male mice (Harlan, Dublin, Va.) were inoculated subcutaneously in the dorsolateral flank region with human glioblastoma cells (DBTRG-05MG) while anesthetized by inhalation of 3% isoflurane (Abbott Laboratories, Abbott Park, Ill.). Mice were housed in individually ventilated cages in groups of five under specific pathogen free conditions and allowed access to sterilized water and food ad libitum. Prior to inoculation, cells were cultivated using standard techniques in DMEM (High-glucose supplemented with L-glutamine; Thermo Scientific, Logan, Utah) containing 10% FBS and 1% penicillin/streptomycin. Upon reaching 80% confluence, cells were suspended at a concentration of 5×10⁶ cells/mL in an 85/15 mixture of PBS and Matrigel (BD Biosciences, San Jose, Calif.). 200 μL aliquots of this final suspension was used for each injection (1×10⁶ cells total).

Tumor growth was measured over time using calipers, and volumes (v) were calculated according to the modified ellipsoid formula (Jensen, M. M., Jorgensen, J. T., Binderup, T. & Kjaer, A. Tumor volume in subcutaneous mouse xenografts measured by microCT is more accurate and reproducible than determined by 18FFDG-microPET or external caliper. BMC medical imaging 8, 16 (2008)):

$\begin{matrix} {v = {l*{\frac{w^{2}}{2}\left\lbrack {mm}^{3} \right\rbrack}}} & \lbrack 18\rbrack \end{matrix}$

where l is the length of the longitudinal diameter and w is the width of the transverse diameter. Tumors were treated when the greatest diameter reached approximately 5 mm; treatment groups are shown in the table in FIG. 44. Mice were anesthetized following the same isoflurane inhalation protocol, and the skin over the tumor was prepped with 70% isopropyl alcohol. Then, custom steel needle electrodes (0.4 mm Ø) were advanced into the center of the tumor. A 0.4 cm spacing (center-to-center) was used in all treatments. In all treatment groups, the pulse generation system was set to deliver its maximum 1000 Vpeak output. The energized time per burst was fixed to 100 μs and bursts were delivered with a repetition rate of 1 Hz for 2 minutes.

Following treatment, topical antibiotic ointment was applied to the needle insertion wounds. Mice were removed from anesthesia and provided 5 mg/kg ketoprofen analgesic diluted in 1 mL sterile saline solution for recovery. The mice were euthanized 30 days post-treatment or earlier for humane reasons if the tumor volume reached 800 mm3.

Samples of any present tumor tissue were excised and sectioned for processing. Representative tissues were preserved in 10% neutral buffered formalin and embedded in paraffin. Formalin preserved paraffin embedded samples were sectioned and processed for histology using hematoxylin and eosin (H&E) staining. All photomicrographs were obtained with a Leica DMI 6000 inverted microscope.

Results

BEAM Treatment Pulse Width, Pulse Number, and Total Energized Time Affect the Lethal Electric Field Threshold

Typical IRE treatments involve the delivery of 80 monopolar pulses, each 100 μs in duration at a repetition rate of 1 Hz. Using the PPT8182 cell line and the same tissue mimic, Arena et al (Arena et al., 2012) found that the lethal threshold for this standard protocol is 501 V/cm. FIG. 40A shows the lethal threshold when the monopolar pulse is replaced by a burst of bipolar pulses with an equivalent electrical dose. The lethal electric field thresholds were found to be 2022, 1687, 1070, 755, 640, 629, and 531 V/cm for bursts containing 0.25, 0.5, 1, 2, 5, 10 and 50 μs pulses, respectively.

The temperature profiles measured were well correlated to those predicted numerically (FIG. 40C). Simulations of these pulses predict a temperature increase of approximately 12° C. at the center of the tissue mimic after 80 pulses were delivered. Experimentally, the average temperature increase across all groups was 14.4±2.2° C. Experiments were conducted at room temperature and the maximum temperature measured experimentally was 34.8° C. The largest variation in maximum temperature, 3.2° C., occurred between the 2 μs and 50 μs groups.

Treatments with 8 and 80 bursts were conducted for bursts with 2 and 50 μs pulses. For comparison, treatments with either 8 or 80 monopolar pulses 100 μs in duration were conducted (FIG. 41A). The thresholds for 8 pulses were found to be 1675, 1211, and 820 V/cm, for the 2, 50, and 100 μs groups, respectively. The corresponding thresholds for 80 pulses were found to be 756, 531, and 501 V/cm.

To explore the limitations of the inventors' equivalent dose approximation, eighty bursts held constant with 2 μs pulses were delivered at three different voltages: 250, 540, and 650 V. For these cases, each burst contained 216, 50, and 32 pulses, resulting in approximate doses of 2000, 2300, and 2200 V²s, respectively. The threshold for cell death for these treatments were 663, 718, and 822 V/cm (FIG. 41B). The 250 and 650 V groups were found to be statistically different with a 99% confidence level (α=0.01).

For bursts with 2 μs pulses, when the voltage was held constant at 540 V, but the energized time per burst was decreased from 100 to 48 or 4 μs, the electric field threshold was found to increase from 718 V/cm to 855 and 1110 V/cm, respectively (FIG. 41C). The difference between 100 and 48 μs was not statistically significant.

FIG. 41D shows the effect of inter-pulse delay on lethal electric field threshold. At 540 V, the inter-pulse delay between 2 μs pulses was increased from 2 μs to 200 μs. Similar to the ‘burst’, this ‘diffuse’ treatment was energized for 100 μs per second and this waveform was delivered for 80 seconds. This change in inter-pulse delay resulted in an increase in electric field threshold from 718 V/cm to 770 V/cm; this difference was not statistically different.

BEAM Treatment Inhibits Tumor Growth In Vivo

At the time of treatment, tumors were on average 91, 101, 45, and 44 mm³ for the sham, 5 μs, 2 μs, and 1 μs groups. Thirty days post-treatment, these averages had changed to 332, 62, 16, and 44 mm³ (FIG. 42E). Three of the four sham tumors more than doubled in size by day 30 (FIG. 42A). The fourth did not significantly increase in size and measured 92 mm³ at the conclusion of the study. Tumors in the 1, 2, and 5 μs group (FIGS. 42B-D) exhibited varying increases in size over days 1-5 before regression was observed. The 1 μs group had two complete regressions at the end of the study. The other two tumors measured 85 and 91 mm³ on day 30. The 2 μs group had 1 complete regression and the other tumor measured 32.9 mm³ on day 30 (FIG. 42C). The 5 μs group had 3 complete regressions. The remaining tumors had volumes of 77, 77, 97, 106, and 144 mm³. FIG. 4E shows the average tumor volumes for each treatment group over the 30 day trial.

Immediately following in vivo treatment, whitening of the tumor occurred. This is associated with reduced blood flow and the beginning stages of edema (FIG. 43B). This characteristic anti-vascular effect of electroporation-based therapies has been utilized in electro-chemotherapy (ECT) to treat bleeding metastasis (Jarm, T., Cemazar, M., Miklavcic, D. & Sersa, G. Antivascular effects of electrochemotherapy: implications in treatment of bleeding metastases. Expert Rev Anticancer Ther 10, 729-746 (2010)). Due to the use of uninsulated electrodes, the skin overlying the tumor was killed in conjunction with the tumor. This resulted in scab formation (FIG. 43C) within 1 day post treatment which typically resolved within two weeks. Endpoint images taken immediately prior to and following tissue harvesting show evidence of complete tumor regression 30 days after BEAM treatment (FIGS. 43D-G).

FIG. 43H-I shows histological sections from the study endpoint of a mouse in the sham group (FIG. 43H) and 5 μs treatment group (FIG. 43I). Despite the fact that no measurable tumor was observed in the treated mouse, pockets of viable glioblastoma cells were present surrounding blood vessels located above the musculature. Similar features were seen in the sham mouse, with the addition of a viable tumor mass beneath the muscle layer. Cells comprising the viable tumor display a large nucleus surrounded by a well-marked cytoplasm and well-defined cell membrane. Additionally, there is evidence of healthy vasculature along the margin of the tumor at the interface between the muscle and fat layer.

Discussion

For bursts of bipolar pulses, the electric field threshold required to induce cell death is inversely correlated to the duration of the constitutive pulses (FIG. 40A). The lethal threshold increases slightly as pulse duration is decreased from 50 μs to 2 μs. The threshold for cell death for bursts with 1 μs pulses is approximately double the threshold for bursts with 50 μs pulses and 250 ns pulses have a threshold approximately four times greater than the 50 μs treatments. The treatments shown in FIG. 40A all received equivalent doses in 80 bursts.

FIG. 40B shows data adapted from Sano et al. (Sano, M. B., Arena, C. B., DeWitt, M. R., Saur, D. & Davalos, R. V. In-vitro bipolar nano- and microsecond electro pulse bursts for irreversible electroporation therapies. Bioelectrochemistry 100, 69-79 (2014) and Arena et al. (Arena et al., 2012) for PPT8182 cells suspended in media and exposed to 80 monopolar 100 μs pulses or 80 bi-polar bursts with pulses between 250 ns and 50 μs (100 μs energized per burst) with a 1500 V/cm voltage-to-distance ratio. In suspension, bursts with 2 μs or shorter pulses do not affect cell viability. In contrast, 1500 V/cm is sufficient to kill all of the cells in the tissue mimics for bursts with pulses 1 μs or longer.

When the cells are in suspension, they take on a more spherical appearance. In contrast, when grown in the 3D tissue mimics they begin to stretch out and obtain a more natural phenotype. In vivo, IRE is typically observed in regions which are exposed to approximately 500-750 V/cm (Garcia, P. A., et al. Intracranial Nonthermal Irreversible Electroporation: In vivo Analysis. Journal of Membrane Biology 236, 127-136 (2010); Miklav{hacek over (c)}i{hacek over (c)}, D., {hacek over (S)}emrov, D., Mekid, H. & Mir, L. M. A validated model of in vivo electric field distribution in tissues for electrochemotherapy and for DNA electrotransfer for gene therapy. Biochimica et Biophysica Acta (BBA)-General Subjects 1523, 73-83 (2000); and Edd, J. F., Horowitz, L., Davalos, R. V., Mir, L. M. & Rubinsky, B. In vivo results of a new focal tissue ablation technique: irreversible electroporation. Biomedical Engineering, IEEE Transactions on 53, 1409-1415 (2006)) and the field strengths predicted in these 3D tissue mimics are more likely to represent the in vivo thresholds for bipolar bursts. However, extensive in vivo evaluation is still needed to determine how these thresholds compare to those necessary to ablate complex heterogeneous tissues such as pancreatic tumors which contain healthy and malignant cells, vasculature, ductile systems, and connective tissue.

Electro-gene (EGT) and ECT protocols typically employ 8 pulses with the goal of permeabilizing the cell membrane, but not inducing cell death. FIG. 41A shows that there is a significant difference between 8 monopolar 100 μs pulses and bipolar 50 μs bursts. This is interesting because these groups were not significantly different when the burst number was increased to 80. Increasing the number of pulses reduced the lethal electric field threshold significantly for all groups. Between 8 and 80 pulses, the thresholds drop by 920 V/cm (55%), 679 V/cm (56%), and 319 V/cm (39%) for the 2 μs bipolar, 50 μs bipolar, and 100 μs monopolar groups, respectively. Interestingly, the lethal thresholds for 80 bursts with 2 μs pulses was the same as 8 monopolar 100 μs pulses. Though not investigated here, the use of bi-polar pulses may allow investigators to treat larger volumes using EGT or ECT without deleterious lethal effects.

Protocols with 1 μs, 500 ns, and 250 ns failed to produce connected lesions in the tissue mimics when the voltage was set to 540 V and the energized time per burst was 100 μs. This made it difficult to accurately calculate the lethal electric field threshold. In the inventors' initial pilot study, the inventors found that increasing the voltage to 650 V while delivering 80 pulses with 100 μs energized time resulted in thermal denaturing of the collagen matrix. Arena et al. (Arena et al., 2012) associated collagen denaturation during IRE with temperatures greater than 45° C. Reducing the energized time to 64 μs at 650 V, a similar dose to 540 V and 100 μs, resulted in well-formed oval shaped lesions for all groups. The present inventors used this higher voltage, equivalent dose protocol for all groups with 1 μs pulses and shorter.

In FIG. 41B the inventors investigated the validity of this equivalent dose hypothesis using bursts with 2 μs pulses, which formed connected lesions at the lowest voltage tested, 250 V. There is no statistical difference between equivalent dose protocols at 650 V and 540 V nor between 540 V and 250 V protocols with a 99% confidence level (α=0.01) and there is no statistical difference between the three groups with a 95% confidence level (α=0.05). This indicates that in the 3D tumor mimic model, an equivalent dose approximation is sufficient for comparing protocols.

It is unclear how far outside this range (250-650 V) the equivalent dose hypothesis is valid. However, clinical IRE systems are currently limited to outputs of 2700 V. At this voltage, a burst energized for 4 μs would have an equivalent dose and a lethal threshold of approximately 750 V/cm (the average of values from FIG. 41B). FIG. 41C shows that when bursts are energized for 100 μs versus 4 μs, there is 35% reduction in the lethal threshold. If these two effects are additive, a protocol with 80 burst of 2 μs pulses, energized for 100 μs per burst (Dose≈58,000 V2s), is expected to have a lethal threshold of approximately 460 V/cm. This indicates that BEAM treatments should be capable of creating similar ablation volumes as the clinical systems currently employed. However, extensive in vivo testing and measurement of ablation volumes will be required to validate this.

Previous in vivo IRE experiments on murine tumor models required the application of pulses with 1000 V_(peak) amplitude or greater to obtain complete regression of similar sized tumors. Neal et al. (Neal II, R. E., et al. Treatment of breast cancer through the application of irreversible electroporation using a novel minimally invasive single needle electrode. Breast cancer research and treatment 123, 295-301 (2010)) achieved complete regression in 5 of 7 mice when 100 monopolar pulses, each 100 μs in duration and 1300 V_(peak) (5600 V/cm) were applied through a bi-polar probe with a 2.3 mm electrode spacing. Al-Sakere et al. (Al-Sakere, B., et al. Tumor ablation with irreversible electroporation. PloS one 2, e1135 (2007)) achieved complete regression in 12 of 13 mice when 80 pulses, each 100 μs in duration and 1000 (2500 V/cm) were applied between plate electrodes spaced 4 mm apart.

To mimic the clinical protocol, treatments in this study were applied through two needle electrodes. A spacing of 0.4 mm was used to maximize coverage of the tumors while accounting for the 1000 V_(peak) limit of the inventors' pulse generation system. The 0.4 mm diameter electrodes used in these in vivo experiments were significantly smaller than the 1 mm diameter electrodes used clinically and the 1.27 mm electrodes used in the tumor mimics. Electrode diameter is closely linked to the electric field distribution and smaller electrodes will produce a smaller ablation zone. To account for this, the number of bursts delivered was increased to 120 to provide the best possible outcomes while avoiding extensive thermal heating effects. Gross and histological examination did not indicate any scar formation from thermal damage.

In the treated groups, the measured tumor volume increased over the first 1-5 days post treatment. The formation of a scab along with the occurrence of edema may have led to an overestimation of tumor volumes during short-term follow-up. Within two weeks after treatment delivery, scabs resolved and evidence of tumor regression was observable.

This treatment protocol inhibited tumor growth. The average tumor volumes in the treatment groups were significantly smaller than control at the end of the study. Due to the limited time-span of the IACUC protocol, it is unclear if the tumors would have entered an exponential growth period post-treatment and the inventors were unable to obtain Kaplan-Meier survival curves. In total, 6 of 14 treated mice had no measurable signs of tumors 30 days after treatment and all protocols were able to achieve some complete regressions. Future work should include a long-term study to monitor tumor regression over the lifetime of the animals.

Histological examination of some treated animals revealed pockets of neoplastic cells superficial to the muscle fascia in the dermal layers, which is indicative of under treatment. It is possible that better regression results can be obtained by using a protocol with a higher applied voltage, increased number of bursts, and/or higher energized time per burst. It is noted that the work presented by Al-Sakere did not obtain a 100% regression rates, however, their protocol has been successfully adapted to human clinical applications with promising results.

Conclusion

This study shows the differences in lethal threshold for IRE and BEAM protocols. Despite delivering equivalent doses, bursts with shorter constituent pulses typically require higher electric field strengths for ablation. The number of bursts, energized time per burst, and pulse duration are all significant factors affecting the lethal threshold. Using 80 bursts the inventors found that 1, 2, and 5 μs pulses had electric field thresholds of 1070, 755, and 640 V/cm. When 200 bursts were delivered in vivo, these pulses had similar effects on tumor volume. All mice treated with BEAM tolerated the therapy well and experienced a significant reduction in tumor volume when compared to untreated controls. Each group attained at least one complete regression. This study provides strong evidence that BEAM can be used for tumor ablation and future investigation is warranted.

Example 4

Methods

Cell Culture

U-87 MG primary human glioblastoma cells (ATCC), D1TNC1 rat astrocyte cells (ATCC), and C6 rat glioblastoma cells (ATCC) were cultured in Dulbecco's Modified Eagle Medium (DMEM) containing 10% fetal bovine serum (FBS) and 1% penicillin/streptomycin (PS) at 37° C. in 5% CO₂ in a humidified incubator. Normal Human Astrocyte (NHA) cells (Lonza) were cultured in Astrocyte Growth Media (Lonza) at 37° C. in 5% CO₂ in a humidified incubator. Cells were seeded in hydrogels at a density of 1×10⁶ cells/mL. The hydrogels were submerged in appropriate growth media for the cell type at 37° C. in 5% CO₂ in a humidified incubator and cell viability was maintained within hydrogels for up to 7 days (FIG. 46A).

Construction of 3D Collagen Scaffolds

Stocks of type I collagen were prepared by dissolving rat tail tendon in acetic acid, followed by freezing and lyophilization as described previously (Arena et al. 2012). Two different stock solution concentrations of collagen were created: 4.5 mg/mL and 30 mg/mL. Scaffolds with a final concentration of 2 mg/mL and 20 mg/mL were made from concentrated collagen stocks to create collagen gels of 0.2% (w/w) and 2% (w/w). Neutralized collagen solutions were created by mixing acid-dissolved collagen with 10×DMEM (10% of total collagen solution volume) and sufficient volumes of 1N NaOH until a pH in the range of 7.0-7.4 was achieved. The neutralized collagen was mixed with cells suspended in DMEM to achieve a cell density of 1×10⁶ cells/mL in the final collagen mixture. Solutions were mixed carefully with a spatula to ensure homogenous distribution throughout the gel without damaging cells. Collagen solutions were then dispensed into a polydimethylsiloxane (PDMS) mold with a cut-out of 10 mm diameter and 1 mm depth and molded flat to ensure consistent scaffold geometry. The inventors' previous mathematical modeling and experiments on oxygen (O₂) consumption rates by tumor cells (Verbridge, S. S. et al. Oxygen-Controlled Three-Dimensional Cultures to Analyze Tumor Angiogenesis. Tissue Engineering. Part A 16, 2133-2141, doi:10.1089/ten.tea.2009.0670 (2010) (“Verbridge et al., 2010”)) confirms that at this cell density and scaffold thickness, O₂ concentration is uniform throughout the scaffold depth. Collagen was allowed to polymerize at 37° C. and 5% CO₂ for 45 minutes.

Construction of 3D Alginate Scaffolds

Calcium alginate gels were created using the same PDMS molds as for collagen, creating discs 10 mm in diameter and 1 mm in thickness. Two alginate gel stock concentrations (0.4% and 4.0% (w/v) were prepared using powdered alginate (Protanal LF 10/60, FMC BioPolymer) that was dissolved in buffer, dialyzed, frozen and lyophilized, followed by re-constitution in serum-free DMEM, as the inventors have previously reported (Verbridge, S. S. et al. Oxygen-Controlled Three-Dimensional Cultures to Analyze Tumor Angiogenesis. Tissue Engineering. Part A 16, 2133-2141, doi:10.1089/ten.tea.2009.0670 (2010)). Alginate concentrations were chosen to span a wide range in mechanical stiffness, similar to the collagen concentrations used. Alginate solutions were mixed with cells at a density of 1×10⁶ cells/mL and dispensed into PDMS molds and molded flat with a porous membrane. Alginate hydrogels were cross-linked by submerging under 0.1M CaCl₂ dispensed over a porous membrane cover for 45 min. The alginate hydrogels were then cultured in 24 well plates with DMEM supplemented with 10% FBS and 1% PS at 37° C., 5% CO₂.

Determination of Shape Factors

U-87, NHA, D1TNC1, and C6 cells were individually seeded in hydrogels of one of the four conditions described previously (0.2%, 2% collagen, 0.4%, 4% alginate). After culturing the cells for 24 hours, the hydrogels were fixed using 4% formalin and blocked and permeabilized using 40 mg/mL bovine serum albumin (BSA) and 0.5% Triton-X. Cellular actin was stained with Alexa Flour 568 phalloidin (Life Technologies, Carlsbad, Calif.) while cell nuclei were stained with diaminophenylindole (DAPI; Sigma-Aldrich, St. Louis, Mo.). Cells were visualized using a Zeiss LSM510 (Carl Zeiss Microscopy LLC, Thornwood, N.Y.) laser scanning confocal microscope. The stained cells were then used to determine cellular shape factors for cells in each of the four conditions. Image analysis was done in Image J (NIH, Bethesda, Md.) to determine the nuclear area, nuclear perimeter, cytoplasmic area, cytoplasmic perimeter, and longest and shortest diameter of the cell. Measurements were made on at least four cells per hydrogel and at least 5 hydrogels were analyzed for each condition.

Live Fluorescent Imaging

U-87 cells were cultured under normal culture conditions and incubated for 16 hours with CellLight Nucleus-RFP, Bacman 2.0 (Molecular Probes, Eugene, Oreg.) and CellLight Tubulin-GFP (Molecular Probes, Eugene, Oreg.) added to the media at a concentration of 10 particles per cell. Cells were then passaged and seeded into hydrogels of a final concentration of 0.2% collagen at a density of 1×10⁶ cells/mL. After cells were cultured in collagen hydrogels for 24 hours, electroporation of hydrogels was performed on the stage of a Zeiss Observer Z1 microscope (Carl Zeiss Microscopy LLC, Thornwood, N.Y.) to allow for imaging during treatment. Images were taken of single cells immediately before pulsing treatments were started and then every 30 seconds for 5 minutes after pulsing began. Cells were imaged upon exposure to IRE treatment or BEAM treatment. Cells that were not exposed to pulses were also imaged as a control.

Electroporation of 3D Scaffolds

Pulsed electroporation experiments were performed in hydrogels with constant electrical properties. The electrical conductivities of each of the gel-cell mixtures were measured with a conductivity meter to ensure similar electrical properties (0.98±0.04 S/m). The IRE pulses were generated using an ECM 830 pulse generator (Harvard apparatus, Holliston, Mass.) and delivered to the tissue through custom electrodes. High-frequency pulses were delivered using a custom-built pulse generation system (INSPIRE 2.0, VoltMed Inc., Blacksburg, Va.). Two solid stainless steel cylinders with diameters of 0.87 mm, separated 3.3 mm edge-to-edge, were used as electrodes.

Treatments were performed delivering a total of 50 square pulses (IRE) or 50 bursts of 1 μs pulses (BEAM). The IRE protocol delivered 100 μs pulses with a repetition rate of 1 pulse per second. In the BEAM protocol, a burst consisting of 100×1 μs pulses with a 5 μs inter-pulse delay was delivered with a repetition rate of 1 burst per second. For IRE treatments, the pulse amplitude was set to 450 V_(peak) while for BEAM treatments 700 V_(peak) was used to produce ablations of approximately the same volume as the IRE group.

Finite Element Analysis in Hydrogels

Finite element models using COMSOL Multiphysics (Version 4.3, COMSOL Inc., Palo Alto, Calif.) were used to solve the Laplace equation to find the electric field distribution within the hydrogels for each different voltage used. COMSOL Multiphysics was also used to solve the Joule heating equation to calculate the temperature distribution in the hydrogel as a result of each treatment. The simulation geometry was modeled as a 10 mm diameter and 1 mm thick cylinder with two steel electrode cylinders (d=0.87 mm) spanning the depth of the hydrogel. The mesh was refined until error between successive refinements was less than 1%. The final mesh contained 47,438 elements and solutions were found in approximately 3 minutes on a Pentium i3 processor.

Finite Element Analysis of Individual Cells

The transmembrane potentials across the cell membrane and nuclear envelope were modeled using a finite element model with an impedance boundary condition scheme (Sano, M. B., Arena, C. B., DeWitt, M. R., Saur, D. & Davalos, R. V. In-vitro bipolar nano- and microsecond electro pulse bursts for irreversible electroporation therapies. Bioelectrochemistry 100, 69-79, doi:DOI 10.1016/j.bioelechem.2014.07.010 (2014)). These finite element models were used to numerically investigate the response of representative cell geometries to simulated IRE and BEAM pulses. Cell geometry was determined based on average measurements made in ImageJ image analysis software (NIH, Bethesda, Md.) from confocal microscopy images. Geometries for U-87 cells in two different collagen densities (0.2%, 2%) as well as four different cell types (U-87, NHA, C6, D1TNC1) in a 0.2% collagen matrix were used. All models were solved using a 2D-axisymmetric platform in COMSOL Multiphysics. A separate electric currents physics module was used for each domain (media, cytoplasm, nucleoplasm). A large media domain, with sides of 300 μm, was used to avoid any significant boundary effects. The cell and the nucleus were modeled as half-ovals where their lengths and widths were varied according to measurements from confocal microscopy images.

Simulations were solved in the time-domain using an electric currents module. To account for the resistance and capacitance posed by the cell membrane and the nuclear envelope the boundaries of the nucleus and cytoplasm were assigned impedance properties based on the existing literature.

Determination of Lethal Thresholds

The thresholds for cell death were determined by first performing a live-dead stain on the hydrogels 24 hours after delivering treatment. Live cells were stained with Calcein AM (Biotium, Hayward, Calif.) and fluoresced as green while dead cells were stained with ethidium homodimer III (Biotium, Hayward, Calif.) and fluoresced as red. The diameter of the red-stained dead region was measured using ImageJ image analysis software. Geometric measurements of the ablation zones were mapped to a finite element model to calculate the electric field during treatments of the scaffolds (FIG. 46C). The electric field magnitude at the edge of the live and dead regions was considered the electric field threshold for cell death for the given cell type.

In Vivo Canine Treatment

All canine in vivo studies were approved by the institutional animal care and use committee (08-218-CVM). IRE treatments were performed in the brains of anesthetized normal canine subjects, and in dogs with spontaneous malignant gliomas according to previously described methods (Edd, J. F. & Davalos, R. V. Mathematical Modeling of Irreversible Electroporation for Treatment Planning. Technology in Cancer Research & Treatment 6, 275-286, doi:10.1177/153303460700600403 (2007) (“Edd and Davalos, 2007”); Garcia, P. A. et al. Non-Thermal Irreversible Electroporation (N-TIRE) and Adjuvant Fractionated Radiotherapeutic Multimodal Therapy for Intracranial Malignant Glioma in a Canine Patient. Technology In Cancer Research & Treatment 10, 73-83 (2011); Rossmeisl, J. H., Garcia, P. A., Roberston, J. L., Ellis, T. L. & Davalos, R. V. Pathology of non-thermal irreversible electroporation (N-TIRE)-induced ablation of the canine brain. Journal of Veterinary Science 14, 433-440, doi:10.4142/jvs.2013.14.4.433 (2013) (“Rossmeisl et al., 2013”)). In tumor-bearing dogs, biopsy of the brain lesion was performed prior to IRE ablation to allow for histopathological diagnosis and grading of tumors, and an additional biopsy of the ablated region obtained within 24 hours of the IRE to characterize the effects of the IRE treatment.

Histomorphological Staining

Archived, paraffin embedded, transversely oriented brain sections from normal and tumor-bearing dogs treated with IRE were retrieved, cut at 5 μm thickness, mounted on positively charged slides, and stained routinely with hematoxylin and eosin (Edd and Davalos, 2007; Rossmeisl et al., 2013). Digital photomicrographs of regions of interest representing IRE ablated regions of cerebral cortex, subcortical white matter, contralateral homologous cortical and white matter controls, and a canine GBM pre- and post-IRE treatment were captured with charge-coupled device digital camera (Nikon DS-Filc, Nikon, Japan) and commercial imaging analysis software system (NIS Elements AR, Nikon, Japan).

Statistical Analysis

Statistical significance was determined by a two-tailed t-test performed in Prism Statistical Software (Version 6, Graphpad, La Jolla, Calif.). A 95% confidence interval was used with significance defined as p<0.05. All numerical results are reported as the mean and the standard deviation of all experimental measurements. No outliers were excluded.

Results

Cell Size Selectivity of Pulsed Electric Fields

Single cell responses to electric field pulses were simulated with finite element modeling. Simulated TMP changes in response to modeled IRE pulses (FIG. 45A) are highly dependent on cell size (FIG. 45B). In contrast, cells exposed to BEAM pulses do not show significant TMP variation with cell size in these models (FIG. 45C).

To experimentally explore the effect of cell size on electric field thresholds for cell death, the inventors tuned the mechanical and chemical structure of the tumor microenvironment using a three-dimensional GBM hydrogel tumor model (FIG. 46A) to then be used as a therapy-testing platform (FIG. 46B). The inventors determined the lethal electric field threshold by simulating the electric field within the hydrogels during pulse exposure, at the two experimental voltages, using finite element modeling (FIGS. 46C and 46D). These simulations reveal the change in expected lesion shape as a function of voltage, evolving from a peanut to a circular shape as the electric field magnitude increases. Finite element modeling of treatment-induced temperature distribution in the hydrogel demonstrates that cellular damage does not occur through thermal effects, as cells are not exposed to temperatures above physiological levels (FIG. 46E), with no long-term temperature increases evident (FIG. 46F).

Cell size and shape within hydrogel scaffolds are functions of scaffold density; by varying collagen density in the tissue model the inventors were able to control cell size and outer membrane perimeter for a single cell type. U-87 MG human GBM cells exhibited a significantly smaller area (p=0.005) in the higher density (2% w/w) collagen (920±249 μm2) as compared with lower density (0.2% w/w) collagen (1572±503 μm2) (FIG. 47A). Using this in vitro model the inventors then determined that these cell geometries determined lethal thresholds for IRE but not for BEAM pulses. As predicted by the model, IRE lesions for cells in 0.2% collagen were larger than the lesions for cells in 2.0% collagen (FIG. 47B, p<0.0001). The larger cells were killed by IRE pulses with amplitude exceeding 428±47 V/cm, while the smaller cells required a larger field for cell death (492±41 V/cm). In contrast, BEAM treatments did not result in statistically significant differences in lesion size, corresponding to an average lethal threshold of 601±65 V/cm that was independent of collagen density (FIG. 47C). The electrical conductivity for the two scaffolds was experimentally comparable, and cell densities were identical in the two conditions.

The inventors performed additional experiments in calcium alginate hydrogels, in which cell morphology is relatively constant for different scaffold densities due to the lack of cell-ECM binding sites (FIG. 48A). In alginate hydrogels, lesion sizes and lethal thresholds were independent of polymer concentration for both IRE (FIG. 48B) and BEAM (FIG. 48C).

In Vivo Selectivity of IRE

The inventors previously treated canine patients with naturally occurring malignant gliomas using IRE29. Histology from this treatment provides an important comparison point between the inventors' 3D in vitro ablation results presented here, and the in vivo outcome in a context that is highly representative of the human GBM phenotype. When untreated cerebrocortical grey matter (FIG. 49A) was exposed to IRE treatment, non-discriminate cell death occurred as both neuronal and glial cells were ablated (FIG. 49B). Similarly, untreated white matter of the internal capsule (FIG. 49C) treated with IRE resulted in glial death in addition to vacuolization and axonal loss. Though malignant glioblastoma cells (FIG. 49E) were ablated with IRE treatment (FIG. 49F), so too is the stromal cytoarchitecture. Based on these in vivo results demonstrating the relatively non-selective nature of IRE ablation in canine GBM, combined with the inventors' in vitro studies demonstrating statistically significant yet small differences in IRE threshold based on cell size, the inventors next focused on the potential for pulsed electric fields to exert cell-specific targeting. Histology images from canine patients illustrate the well-known tumor cell phenotype characterized by the enlarged nuclei of GBM cells (FIG. 49E) compared to healthy tissue (FIGS. 49A, C), therefore motivating the inventors' hypothesis that intracellular localization of treatment electric fields may enable tumor cell targeting due to nuclear size differences.

Intracellular Effect of Pulsed Electric Fields

To examine the potential for BEAM pulses to exert their effect via intracellular localization of electric fields, the inventors performed finite element modeling of field distribution across a single cell. This model predicts that for a simulated IRE pulse with an electric field magnitude of 500 V/cm applied for 100 μs, only 14% of the external electric field traverses the cell membrane and is present in the cytoplasm (FIG. 50A). In contrast, BEAM pulses deliver most of their energy to the inside of the cell (FIG. 50B). The cytoplasm is charged over 400 V/cm for the entire duration of each 1 μs BEAM pulse while the same is true for only 8% of each 100 μs IRE pulse. To test the implications of effects on tumor cell nuclei for this prediction of a strong intracellular field created by BEAM, the inventors constructed 3D models using four different cell types (FIG. 50C), chosen to include multiple malignant versus normal cell comparisons. These 3D cultured cells exhibited no significant difference in cell area (FIG. 50D), but did exhibit significant differences in nuclear area (FIG. 50E). A human malignant glioma cell line (U-87) showed significantly greater nuclear area than normal human astrocytes (NHA) (p=0.0048) while a rat glioblastoma line (C6) exhibited increased nuclear area when compared to normal rat astrocytes (D1TNC1) (p=0.0140).

Consistent with model predictions of IRE cell size dependence and nuclear size independence, the four cell types exhibited similar IRE lesions (FIG. 51A). In contrast, BEAM lesions in the tissue mimics with GBM cells were significantly larger than lesions with normal astrocytes (FIG. 51B). The similar lethal IRE thresholds across cell types (FIG. 51C) is consistent with the fact that all four cell types have similar outer membrane areas. BEAM experimental results, however, reveal a lower lethal threshold for malignant cells (FIG. 51D), which have larger nuclei compared with their normal cell counterparts. For BEAM treatments on human cells, U87 glioblastoma cells were killed at a threshold of 601+/−71 V/cm while NHAs were killed at a threshold of 1006+/−81 V/cm (p<0.0001). For rat cell lines, C6 cells had a lethal threshold of 752+/−58 V/cm while D1TNC1 cells had a lethal threshold of 1107+/−106 V/cm (p<0.0001).

Death Mechanisms of IRE and BEAM

To investigate the differences between the mechanism of death with IRE and BEAM the inventors performed single cell imaging upon exposure to each treatment regime. Cell nuclei and tubulin were stained by live fluorescent stain and cultured in 3D collagen hydrogels. Fluorescent imaging in situ within these hydrogels was performed directly before, and then at 30-second intervals after exposure to IRE, revealing an outward diffusion of dye from the cell membrane within 1 minute after pulsing (FIG. 52A). By 5 minutes after treatment the tubulin dye had diffused almost entirely out of the cell while the nuclear dye showed a disruption of the integrity of the nucleus. In contrast, cells exposed to BEAM showed a strong inward collapse of the nucleus followed by a collapse of the tubulin stained cytoplasm on the 5-minute timescale (FIG. 52B). A control cell that was not exposed to either treatment imaged over the same time course confirms that treatment-induced changes are not related to photo-bleaching (FIG. 52C).

Estimate of Lethal Threshold for Nuclear Disruption

The inventors explored the relationship between BEAM lethal thresholds and nuclear size, leveraging the experimental data as input for subsequent mathematical models. Based on this data, it would appear that cell death occurs at a critical nTMP disruption that is independent of cell type, whereas the external field required for this nuclear disruption scales inversely with nucleus size. Using experimental findings for lethal thresholds, nuclear geometries, and idealized cell geometries for glioma cells and astrocytes, the inventors performed finite element modeling of single cell response to minimum lethal electric fields for each cell type. Simulating cell exposure to these lethal conditions, 1006 V/cm for NHA cells and 601 V/cm for U-87 cells, the inventors found a larger increase in TMP for the glioma cell than for the astrocyte (FIG. 53A), however these TMPs were significantly below the anticipated 1 V instantaneous lethal threshold for IRE. In contrast, simulation of nTMP response predicts similar increases in nTMP for both cell types, indicating that cell death is occurring at a common value of nTMP for both cells, at ˜130 mV disruption (FIG. 53B).

Discussion

The overall goal was to leverage tissue engineered models of tumor versus normal brain microenvironments, based on previously published methods (Verbridge, S. S. et al. Oxygen-Controlled Three-Dimensional Cultures to Analyze Tumor Angiogenesis. Tissue Engineering. Part A 16, 2133-2141, doi:10.1089/ten.tea.2009.0670 (2010)), to investigate the response of representative cell geometries to IRE and BEAM pulses. These platforms critically provide a three-dimensional physiological tissue context in which to explore the effects of 3D cell morphology on response to electric fields, not possible with 2D experiments, while eliminating other confounding variables found in vivo. Hydrogels have been previously established as a relevant platform to test tissue responses to IRE pulses (Arena et al., 2012), while such models have also been demonstrated to better recapitulate human tumor physiology and therapy response as compared with 2D models (Fischbach, C. et al. Engineering tumors with 3D scaffolds. Nat Meth 4, 855-860, (2007); Fong, E. L. S. et al. Modeling Ewing sarcoma tumors in vitro with 3D scaffolds. Proceedings of the National Academy of Sciences 110, 6500-6505, doi:10.1073/pnas.1221403110 (2013)). With the ability to easily tune targeting parameters and microenvironment, these models provide a valuable tool for measuring the impact of cell morphology and tissue physics on therapy response broadly, and more specifically on response to therapeutic electric fields.

It is important to note that the inventors' work is informed by, and builds on their experience in treating spontaneous GBM in canine patients. Spontaneous, primary brain tumors are only relatively common in two species—dogs and humans. Human and canine brain tumors share many features, including histopathologic and diagnostic imaging characteristics, which allows application of World Health Organization pathologic classification and imaging based therapeutic response assessment schemes used in human clinical practice. Canine and human brain tumors have also been demonstrated to have similar expression patterns of growth factor receptors, chromosomal deletions, and losses of function of tumor suppressor genes. As tumors progress 5- to 7-fold faster in dogs relative to humans, dogs with spontaneous brain tumors are an attractive model for the faithful and rapid evaluation and translation of novel brain tumor therapeutics (Rossmeisl, J. H. New Treatment Modalities for Brain Tumors in Dogs and Cats. Veterinary Clinics of North America: Small Animal Practice 44, 1013-1038, doi:http://dx.doi.org/10.1016/j.cvsm.2014.07.003 (2014)).

Size selective ablation using PEFs has been previously reported for cell suspensions, differentiating tumor from blood cells based on large differences in size (Eppich, H. M. et al. Pulsed electric fields for selection of hematopoietic cells and depletion of tumor cell contaminants. Nature Biotechnology 18, 882-887, doi:http://dx.doi.org/10.1038/78504 (2000) (“Eppich et al., 2000”)), but has yet to be demonstrated for cells cultured in physiologically-relevant tissues. The inventors' experiments support the concept that IRE results in cell size-selective lethal thresholds into 3D tissues. The bulk electrical resistance properties of the cell-seeded hydrogels did not vary as a function of collagen density, and the inventors therefore believe differences measured are a result of cell morphology rather than altered tissue electrical properties. Control experiments performed in alginate further support this hypothesis that the differences observed in collagen resulted from cell size variations rather than additional factors such as direct sensing of matrix density. Although this finding does not eliminate the possibility that variation in binding ligand density may also impact lesion size, this size dependence is consistent with previously published data on cells in solution (Eppich et al., 2000). Furthermore this correlation of threshold with cell size is absent for BEAM. The inventors hypothesize that this is due to the BEAM field primarily interacting with the inner organelles of the cell. The inventors' finite element modeling confirms this hypothesis as a single BEAM burst applied to a single cell model produces a much higher field inside the cell than a simulated IRE burst. BEAM treatment delivers a rapid burst of over 100 of these 1 μs pulses. This allows BEAM pulses to preferentially charge intracellular membranes, which the inventors anticipated would have profound effects on cell death as a function of cell type.

The inventors' in vitro 3D model results demonstrate a statistically significant dependence of field threshold on cell size, however the cell size heterogeneity observed in vivo may prevent this dependence from being leveraged for targeting specificity. A much more obvious difference between cell types, clearly evident in the inventors' H&E staining of tumorous and healthy canine brain samples, is the enlarged nuclei of cancer cells compared to healthy brain tissue. Used as a pathological indicator of cancer, enlarged nuclei compared with their non-malignant counterparts is one of the most reliable distinguishing characteristics of tumor cells (Zink, D., Fischer, A. H. & Nickerson, J. A. Nuclear structure in cancer cells. Nat Rev Cancer 4, 677-687 (2004)), however the targeting of anti-cancer therapy against this hallmark has never been demonstrated.

The nucleus is typically the largest contiguous intracellular feature and a likely target for damage by the high intracellular fields produced by BEAM. To experimentally test the effect of nuclear area on treatments, the inventors chose different cell types, which exhibited differences in nuclear sizes without significant differences in plasma membrane area, eliminating confounding effects due to cell size. Numerical simulations identified increased nuclear size as an important variable for increased nTMP. An increase in nTMP could trigger cell death above a specific threshold, and therefore malignant cells should have a lower BEAM lethal threshold than normal cells, in contrast with IRE, which would not exhibit nuclear selectivity. The similarity of IRE thresholds is consistent with the fact that there was no significant difference in plasma membrane areas. The differences in BEAM lesion sizes supports that BEAM threshold differences are related to nucleus area as opposed to overall cell area, with lower lethal thresholds corresponding to larger nuclei. The intracellular field produced from BEAM seems to affect the intercellular nucleus membrane in a way at least partially analogous to the way IRE affects the plasma membrane, as a larger membrane exposed to the majority of the electric field is easier to affect than a smaller membrane.

Time-course images of single cells exposed to each treatment show a distinct difference in mechanism of killing between BEAM and IRE, consistent with the findings that different cellular characteristics are important variables with the two treatments. The time-course of cell death after IRE treatment strongly implicates the immediate disruption of the cell membrane as a cause of cell death, as tubulin proteins originally confined in the cell by the cell membrane begin diffusing out of the cell upon exposure to IRE. In contrast, cells exposed to BEAM show no diffusion from the outer cell membrane but rather a nuclear collapse while the tubulin is retained within the original cell area. These finding suggest that the outer membrane does not play as much of a role in the mechanism of cell death in BEAM, but rather that the primary effect is on the nucleus.

Given the inventors' results, it appears BEAM is acting on the biophysical structure of the cells in a way that nuclear area becomes a key variable. When glioma and astrocyte cells were simulated at their respective lethal BEAM thresholds (601 V/cm vs. 1006 V/cm), the inventors found similar TMP and nTMP ranges of approximately 150-250 mV and 100-130 mV, respectively. These simulations did interestingly predict a small difference in outer TMP as a function of nuclear size. However the magnitude of this TMP, approximately 150 mV, was significantly lower than the anticipated instantaneous threshold (1 V) for cell death by irreversible electroporation. Thus, it would appear that the primary mechanism of death with BEAM is not an increase in cell TMP, but rather is related to intracellular effects. For glioma and astrocyte cells, the maximum simulated nTMP of 130 mV is also well below the lethal threshold for death resulting from outer membrane disruption, suggesting that small disruptions of nTMP may significantly impact cell survival. It is unclear whether the pathway to cell death is dominated by effects on the nuclear envelope alone, versus in combination with cell membrane disruption, or a separate cascade of intracellular effects. However, the correlation of nTMP values between the two different cell types, at different lethal electric field strengths, indicates that nuclear area impacts the cell death process after BEAM treatment.

The inventors' mathematical model does have limitations, as outer cell membranes are approximated as elliptical, and do not account for the irregular shape of physiological cells, or heterogeneity in electrical properties of individual cells. Inclusion of membrane conductivity changes due to electroporation effects is expected to enhance the accuracy of the inventors' simulations. While experimental evidence also suggests that outer membrane electroporation is occurring during BEAM (at time-points beyond those in FIGS. 52A-C, data not shown), the inventors' experimental results and model findings strongly suggest an active role for nTMP effects in the BEAM mechanism of action. It is widely recognized that the mechanism of death in irreversible electroporation using short pulses is complex, poorly understood, and can follow multiple different pathways (Weaver, J. C., Smith, K. C., Esser, A. T., Son, R. S. & Gowrishankar, T. R. A brief overview of electroporation pulse strength-duration space: A region where additional intracellular effects are expected. Bioelectrochemistry 87, 236-243, doi:http://dx.doi.org/10.1016/j.bioelechem.2012.02.007 (2012)). Furthermore, nuclear poration may be aided not only by increased nuclear size of cancer cells but also other abnormalities of the nucleus such as reduced nucleus stiffness necessary for invasion (Dahl, K. N., Ribeiro, A. J. S. & Lammerding, J. Nuclear shape, mechanics, and mechanotransduction. Circulation research 102, 1307-1318, doi:10.1161/CIRCRESAHA.108.173989 (2008)). Another possibility is an amplification of the electric field applied to the cytoplasm caused by distortion around an enlarged nucleus. This may result in other inner organelles, such as mitochondria, being disrupted by BEAM pulses. The inventors' results highlight the importance of TMP increases in both IRE and BEAM and nTMP increases specifically associated with BEAM, in determining cell death PEF thresholds.

It is important to note, the death mechanism of IRE and BEAM are not based on targeting the highly proliferative phenotype that is leveraged by many current GBM therapies including chemotherapy and tumor treating fields (Kirson, E. D. et al. Alternating electric fields arrest cell proliferation in animal tumor models and human brain tumors. Proceedings of the National Academy of Sciences 104, 10152-10157, doi:10.1073/pnas.0702916104 (2007)). While these therapies leave behind quiescent tumor initiating cells that cause recurrence, IRE and BEAM should elicit a death response through membrane disruption for both bulk tumor cells and tumor initiating cells. It is unlikely that this physical death mechanism would select for the emergence of resistant subpopulations on short timescales, because a large number of genetic mutations would likely be required to render a cell resistant to electric field-induced damage.

Though the exact mechanism of cell killing with BEAM is not yet known, the inventors' modeling and experimental data suggest a mechanism that is different than that of long IRE pulses which target the plasma membrane, and that, unlike for IRE, is cell type dependent among cells of similar size. The BEAM killing mechanism is such that the biophysical structure of malignant cells allows for the selective targeting of these cells using a range of electric field distributions that induce no damage to the healthy cells studied but elicit a death response in malignant cells. Because malignant cells that comprise the bulk tumor have a lower death threshold (˜530-810 V/cm) than normal astrocytes (˜930-1200 V/cm) surrounding the tumor, it follows that a treatment regime delivering a voltage between these two thresholds to the edge of the tumor may result in ablation of tumor cells while sparing healthy astrocytes. A threshold in such a range at the edge of the tumor may be effective at killing the invasive glioblastoma cells that render surgery to be an ineffective treatment for GBM, and infiltrative tumors more broadly.

Example 5

Individual pulses with durations one to two orders of magnitude shorter than IRE pulses can kills cells in such a way that is less dependent on the outer cell diameter (assuming a similar size nucleus). The individual pulses are applied in alternating polarity to reduce muscle contractions. Additionally, the individual pulses are repeated to form a high-frequency burst, and multiple bursts are typically necessary to induce cell death. This is similar to how multiple, longer duration pulses are applied during an IRE treatment. This form of BEAM treatment typically requires a higher e-field threshold, but there is less dependence on cell size. Therefore, treatment planning is significantly reduced, as different cell types, regardless of their morphology, have the same e-field threshold.

In the theoretical example provided in FIGS. 54A-D, the cells are assumed to be spherical, and the conductivities λo and λi are set to 0.1 S/m and km is set to 3e-7 S/m. The plots of FIGS. 54A-D show the TMP at the cell pole (θ=0) for a cell with a diameter of 10 um (solid line) and a cell with a diameter of 15 um (dotted line). As shown in FIGS. 54A-B, the cells are exposed to BEAM with 500 ns long pulses applied at 2000 V/cm. As shown in FIGS. 54C-D, the cells are exposed to IRE with 5 us long pulses applied at 1250 V/cm. Because the BEAM pulses are shorter than the membrane charging time, the peak TMP reach at the end of the pulses is nearly the same for both cell diameters. During IRE, the outer membrane is fully charged and the TMP reaches a plateau that is significantly different for each.

The present invention has been described with reference to particular embodiments having various features. In light of the disclosure provided above, it will be apparent to those skilled in the art that various modifications and variations can be made in the practice of the present invention without departing from the scope or spirit of the invention. One skilled in the art will recognize that the disclosed features may be used singularly, in any combination, or omitted based on the requirements and specifications of a given application or design. When an embodiment refers to “comprising” certain features, it is to be understood that the embodiments can alternatively “consist of” or “consist essentially of” any one or more of the features. Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention.

It is noted in particular that where a range of values is provided in this specification, each value between the upper and lower limits of that range is also specifically disclosed. The upper and lower limits of these smaller ranges may independently be included or excluded in the range as well. The singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. It is intended that the specification and examples be considered as exemplary in nature and that variations that do not depart from the essence of the invention fall within the scope of the invention. Further, all of the references cited in this disclosure are each individually incorporated by reference herein in their entireties and as such are intended to provide an efficient way of supplementing the enabling disclosure of this invention as well as provide background detailing the level of ordinary skill in the art. 

1. A method of selectively treating cells, comprising: applying to a tissue a plurality of electrical pulses with a delay between successive pulses, wherein the length of each pulse and the delay between successive pulses are optimized to produce a first treatment zone and a second treatment zone; wherein only selected cells are affected in the second treatment zone.
 2. The method of claim 1, wherein the applying is performed in vitro.
 3. The method of claim 1, wherein the applying is performed in vivo.
 4. The method of claim 1, wherein the applying is performed ex vivo.
 5. The method of claim 1, wherein within the second treatment zone cancer cells are inhibited by way of slowed or arrested cell division.
 6. The method of claim 1, wherein within the second treatment zone cancer cells are inhibited by way of slowed or arrested migration.
 7. The method of claim 1, wherein within the second treatment zone cancer cells are inhibited by way of reduced transport of blood and nutrients.
 8. The method of claim 1, wherein within the first treatment zone cancer cells and non-cancer cells are killed by necrosis.
 9. The method of claim 1, wherein within the second treatment zone cancer cells are killed by apoptosis.
 10. The method of claim 1, wherein some cancer cells and some non-cancer cells are killed in the first treatment zone.
 11. The method of claim 1, wherein some cancer cells are killed or inhibited in the second treatment zone and some non-cancer cells are spared in the second treatment zone.
 12. The method of claim 8, wherein both cancer cells and non-cancer cells are killed within the first treatment zone as a result of an increase of their transmembrane potential to a lethal threshold.
 13. The method of claim 5, wherein cancer cells are killed within the second treatment zone as a result of an increase in their nuclear transmembrane potential to a lethal threshold.
 14. The method of claim 1, wherein the delay between successive pulses is greater than the length of each pulse.
 15. The method of claim 1, wherein the delay between successive pulses is a fraction of the length of each pulse.
 16. The method of claim 1, wherein the selected cells are cancer cells and the length of each pulse is equivalent to the charging time of the cell membrane of the cancer cells plus the discharge time of the nuclear membrane of the cancer cells, while the delay between successive pulses is equivalent to the charging time of the cell membrane of the cancer cells.
 17. The method of claim 16, wherein the charging time of the cell membrane of the cancer cells and the discharge time of the nuclear membrane of the cancer cells are determined through numerical modeling.
 18. The method of claim 1, wherein the plurality of electrical pulses comprises an electric field waveform which is a rectangular pulse, ramp, decaying exponential, or sine wave.
 19. The method of claim 18, wherein the electric field waveform is unipolar or bipolar.
 20. The method of claim 18, wherein the electric field waveform is a superimposed, bimodal signal comprising a first frequency harmonic and a second frequency harmonic, wherein the second frequency harmonic has a frequency higher than that of the first frequency harmonic.
 21. The method of claim 18, wherein the electric field waveform comprises alternating nanosecond-order pulses with microsecond order pulses in succession.
 22. The method of claim 18, wherein the electric field waveform is asymmetric.
 23. The method of claim 18, wherein the electric field waveform has a carrier frequency in the range of 100 kHz to 10 MHz.
 24. The method of claim 18, wherein carrier frequency or pulse duration of the waveforms are based on the cross-over frequency of the cancer cells.
 25. The method of claim 1, wherein the length of each pulse and the delay between successive pulses are optimized based on the physical nucleus to cytoplasm size ratio of the cancer cells.
 26. The method of claim 1, wherein the pulses are bipolar square waves and the length of each pulse is between 250 nanoseconds and 50 microseconds. 27-38. (canceled)
 39. A system for selectively treating cells, comprising: at least one electrode; and a voltage pulse generator coupled to the electrode and configured to apply a pulse train comprising a plurality of electrical pulses, wherein the pulse train has an electric field waveform which is a superimposed, bimodal signal comprising a first frequency harmonic and a second frequency harmonic, wherein the second frequency harmonic has a frequency higher than that of the first frequency harmonic.
 40. The system of claim 39, wherein the voltage pulse generator is configured to select the bimodal signal such that the pulse train selectively kills cells of a selected type and spares cells of another type. 41-44. (canceled)
 45. A method of selectively treating cells, comprising: applying a plurality of electrical pulses to a substance containing cells, wherein the plurality of electrical pulses has a frequency, amplitude, and pulse waveform selected to treat target cells of one type of cell and spare non-target cells of another type of cell; determining a nucleus-to-cytoplasm ratio for the target cells; and selecting the frequency, amplitude, and pulse waveform based on the nucleus-to-cytoplasm ratio for the target cells.
 46. The method of claim 45, wherein the substance containing cells is a tissue.
 47. The method of claim 45, wherein the applying is performed in vitro.
 48. The method of claim 45, wherein the applying is performed in vivo.
 49. The method of claim 45, wherein the applying is performed ex vivo.
 50. The method of claim 45, a selective method wherein cancer cells are treated and normal cells are spared.
 51. The method of claim 45, a palliative method wherein cancer cells of a more malignant type are treated and cancer cells of a less aggressive type are spared.
 52. A method of selectively ablating malignant cells, the method comprising: determining a first death threshold for malignant cells present in a tissue region; determining a second death threshold for non-malignant cells present in the tissue region; administering electrical pulses to the tissue region at or above the first death threshold and below the second death threshold to kill the malignant cells.
 53. The method of claim 52, wherein the non-malignant cells are not killed.
 54. The method of claim 52, wherein the malignant cells each comprise a cell nucleus and are killed by administering the electrical pulses in a manner sufficient to disrupt the cell nucleus.
 55. The method of claim 1, wherein the second treatment zone surrounds a tumor and the selected cells are infiltrative cancer cells originating from the tumor.
 56. The method of claim 55, wherein the tissue is brain tissue and the tumor is glioblastoma.
 57. (canceled)
 58. The method of claim 45, wherein the nucleus-to-cytoplasm ratio is measured from cells taken from a biopsy of the substance containing cells. 59-66. (canceled)
 67. The method of claim 1, wherein the cells affected by the plurality of electrical pulses in the second treatment zone have a higher nucleus-to-cytoplasm ratio than cells not affected by the plurality of electrical pulses in the second treatment zone. 